STAT 101Topics: Syllabus, Nature of StatisticsHandouts: Green Sheet #1; Syllabus; Assignment Schedule; Anatomy of Statistics (2): 1) Statistical Alphabet, 2) Statistical RelationshipsOnline: All handouts; PowerPoint for the Nature of StatisticsCourse Assignments:

1) Review text (see syllabus for options). Scan through text for general format, etc. Review: Ch. 1, section 1.12) Go online to the Anatomy of Statistics link and look at a couple of these documents.3) Go online, scan through the SPSS Manual Procedures section to get an idea of the current manual’s format. 4) Items below

Next Class: Nature of Statistics – Terminology (cont.)Stat Essentials (What I should know from today): Be able to: 1) define “Data”; 2) define a “Variable”; 2) distinguish between objective (response/dependent) and explanatory (independent) variables; 3) identify variables to be studied when provided a study scenario; 4) other terms if we get there; and 5) syllabus.

Problem 1.1: Nutrition According to a study published in the Journal of the American Dietetic Association:CHICAGO – The intake of added sugars in the United States is excessive, estimated by the US Department of Agriculture in 1999-2002 as 17% of calories a day. Consuming foods with added sugars displaces nutrient-dense foods in the diet. Reducing or limiting intake of added sugars is an important objective in providing overall dietary guidance. In a study of nearly 30,000 Americans published in the August 2009 issue of the Journal of the American Dietetic Association, researchers report that race/ethnicity, family income and educational status are independently associated with intake of added sugars. Groups with low income and education are particularly vulnerable to eating diets with high added sugars. [For Release August 4, 2009; excerpt from ADA webpage 8.26.2009]

1. Identify an objective variable for this study. What values could this variable assume?

2. Identify three explanatory variables. What values could these variables assume?

Problem 1.2: Diet Calcium & Blood PressureA heart researcher is interested in studying the relationship between diets which are high in calcium and blood pressure in adult females. The researcher randomly selects 20 female subjects who have high blood pressure. Ten subjects are randomly assigned to try a diet which is high in calcium. The other ten subjects are assigned to a diet with a standard amount of calcium. After one year the average blood pressures for subjects in both groups will be measured and compared to decide if diets high in calcium decrease the average blood pressure.

1. Identify an objective variable for this study and its associated values.

2. Identify some potential explanatory variables and their associated values (may not be specifically identified in the paragraph).

Problem 1.3: Get Married - Gain WeightResearcher Penny Larson and her associates wanted to determine whether young couples who marry or cohabitate are more likely to gain weight than those who stay single. The researchers followed 8,000 men and women from 1995 through 2002 as they matured from the teens to young adults. When the study began, none of the participants were married or living with a romantic partner. By 2002, 14% of the participants were married and 16% were living with a romantic partner. At the end of the study, married or cohabitating women gained, on average, nine (9) pounds more than single women, and married or cohabitating men gained, on average, six (6) pounds more than single men. [p21sullivan]

1. Identify an objective variable for this study and its associated values

2. Identify an explanatory variable and its associated values.

Problem 1.4: Obesity and Artery CalcificationScientists were interested in learning if abdominal obesity is related to coronary artery calcification (CAC). The scientists studied 2,951 participants in the Coronary Artery Risk Development in Young Adults Study to investigate a possible link. Waist and hip girths were measured in 1985-86, 1995-96 (year 10) and in 2000-01 (waist girth only). CAC measurements were taken in 2001-02. The results of the study indicated that abdominal obesity measured by waist girth is associated with early atherosclerosis as measured by the presence of CAC in participants. [p21sullivan]

1. Identify an objective variable for this study and its

2. Identify an explanatory variable and its associated values.

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STAT 101

TOPICS: Nature of Statistics Terms and RelationshipsDOCUMENTS:

HANDOUTS: Green #2; Yellow worksheet #1& 2: 1) Top Films and 2) Twenty-Five Q’s classification

AVAILABLE ONLINE: All handouts listed aboveASSIGNMENT:

Readings: Ch. 1: sections 1.1 & pages10-13; 17-20 (skipping the TI instructions) Problems: p. 53 #53-64 Finish Worksheets #1 - Top Films and #2 - Twenty-Five Questions Items below

NEXT CLASS: Nature of Statistics: Sampling, etc.Stat Essentials (taken from today): Be able to: 1) define terms and relationships as presented on the sheet Anatomy of the Basics: Statistical Terms and Relationships; 2) identify variables and their characteristics

Problem 2.1:

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An 8x12, 20 page Shutterfly photo book costs $29.00. How much would it cost given the above discount?

Problem 2.2: A heart researcher is interested in studying the relationship between diets which are high in calcium and blood pressure in adult females. The researcher randomly selects 20 female subjects who have high blood pressure. Ten subjects are randomly assigned to try a diet which is high in calcium. The other ten subjects are assigned to a diet with a standard amount of calcium. After one year the average blood pressures for subjects in both groups will be measured and compared to decide if diets high in calcium decrease the average blood pressure.

1) Identify the population.

2) What characteristic (variable) of the population is being measured?

3) Identify the sample.

4) Is the purpose of this data collection to perform descriptive or inferential statistics? [P15#1H&M]

5) Could blood pressure be used as an explanatory variable in this situation?

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Problem 2.3:Heroin Use: The National Center for Drug Abuse is conducting a study to determine if heroin usage among teenagers has changed. Historically, about 1.3 percent of teenagers between the ages of 15 and 19 have used heroin one or more times. In a recent survey of 1,824 teenagers, 37 indicated they had used heroin one or more times.

1) Identify the population.

2) Identify a variable of interest.

3) Identify a sample.

4) Is the purpose of this data collection descriptive or inferential?

Problem 2.4:Cell Phone Frau d : Lambert and Pinheiro (2006) described a study in which researchers try to identify characteristics of cell phone calls that suggest the phone is being used fraudulently. For each cell phone call, the researchers recorded information on its direction (incoming or outgoing), location (local or roaming), duration, time of day, day of week, and whether the call took place on a weekday or weekend. [WSed3p6]

1) Identify the observational units in this study.

2) Identify the qualitative variables and their characteristics.

3) Identify the quantitative variables and their characteristics.

4) Would call duration be a good explanatory variable? Why/why not?

Problem 2.5:Student Characteristics: A Case represents all of the information collected from one source, such as a student.Student #1 is a male who does not smoke, who lives in an urban area, and who would prefer to win an Olympic gold medal over an Academy Award or Nobel Prize. He indicates that he exercises 10 hours a week, watches television one hour per week, and has a GPA of 3.33. A resting pulse rate of 58 beats per minute, the oldest of three children and a desire to become a fireman represent other characteristics of this student.

Identify the variables for which data were obtained and classify them as qualitative (categorical)/quantitative, discrete/continuous, and provide a measurement level for each variable.

If similar information were obtained from 49 other students, which variables might most likely be used as explanatory variables?

Problem 2.6:Iceland: According to World Bank data, 90% of Icelanders have access to the Internet. In order to determine this value, what were the units from which this figure was obtained? What was the variable of interest (objective variable) and what were the values of this variable? Identify the variable’s characteristics (Qual/Quant etc.) (L5p.7)

If one were to look at the number of people worldwide with access to the Internet, we could record the proportion within each country. In doing so, what would be the population units? What was the variable of interest (objective variable) and what were the values of this variable? Identify the variable’s characteristics (Qual/Quant etc.)

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STAT 101

TOPICS: Sampling; Combinations (?)DOCUMENTS:

HANDOUTS: Green #3; Yellow #3: Sampling AVAILABLE ONLINE: Green #3; Yellow #3: Sampling; PowerPoint placed online (3): 1)

Sampling; 2) Experimental Design; 3) Combinations & PermutationsASSIGNMENTS:

Text Readings: Ch. 1: pp. 17-20 (sampling); Text Problems: p. 54 #71-73, 75 Extra Credit #1 (optional) Items below

NEXT CLASS: TOPICS: Combinations etc. (?); Qualitative Data; DUE: ExCr#1Stat Essentials (taken from today): Be able to: 1) identify sampling approaches; 2) understand relationships among basic statistical terms; 3) distinguish between combinations & permutations. Problem 3.1: The grade for this course is based upon 400 points. These points are converted to a 100-point base to result in a final course grade.

1. How many of the 400 points represent one point of the final grade?

2. Extra credit points are added to those you have accrued throughout the course via exams, etc. If you complete ten extra credit exercises, and receive full credit for them all (i.e. 10 points), by how many points will your final grade increase?

3. Over the course of the semester Elijah elects to not submit three, 10-point class assignments. By how many points would his final grade decrease as a result of not having submitted these three assignments?

Problem 3.2: Burglaries: ADT Security Systems advertised that “when you go on vacation, burglars go to work.” Their ad stated that “according to FBI statistics, over 26% of home burglaries take place between Memorial Day and Labor Day.” What is misleading about this statement? (Triola7ed,p15#6)

Problem 3.3: Election: Review the cartoon to the right. Assume that there are 100 boys and 100 girls. Demonstrate using these 200 students how this student’s conclusion is either correct or incorrect. Present your answer using both numerical computations and sufficient discussion to support your findings.

Problem 3.4: Variables: Identify the explanatory and objective variables in the following pairs of variables.

A) Lung capacity and number of years smoking cigarettes

B) Blood alcohol content and the number of alcoholic drinks consumed

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C) Year and world record time in a marathonProblem 3.5: O-Tiger price hike: For many years Oneonta had a single-A farm team of the NY Yankees, which was followed by a farm team of the Detroit Tigers. When the Tigers arrived, the prices for seating changed. The following comes from an editorial in the local newspaper about the rise in ticket prices for the local single-A professional baseball team. “General admission season passes for adults will be $155, up from $70, in 2009, while six-seat boxes will go up 500 percent, from $300 to $1,500.” (source: The Daily Star, In Our Opinion column for Feb. 7 & 8, 2009, p D3; this team has since left town)

A) The $85 increase in the single seat price represents how much in terms of a percentage increase?

B) Demonstrate using a numerical analysis whether or not the cost of a six-seat box increased by 500%.

Problem 3.6: Seat Belts: Suppose that there are 300 students taking statistics and that they are asked if they always use seat belts.

A) If 27% of the students indicate that they do not always use seat belts, how many students is this?

B) Suppose that in different course 20% of the students do not use seat belts and that the 20% represents 43 students. How many students are in this class?

Problem 3.7: SPSS: Data File: Environmental_Sustainability_sp2013.savFinding the data file: Go to my web page > Stat 101: Intro > Data Files > open the file noted above How to obtain Selected Tables and Charts:

Frequency Table: Analyze > Descriptive Statistics > Frequency > move variable to right cell > Ok.Bar Chart: Graphs > Legacy Dialog > Bar> Define (leave as is) > move variable to Category Axis cell > OKREFERENCE: SPSS Manual available online1) Make a frequency table of the variable, e1, which represents opinions of whether or not the earth is reaching the

population limit it can support. Place your name in the table by including a footnote. [Note1: Footnote: double-click on the table, select Insert from the top menu> footnote.] [Note2: when making a table or chart, if you cannot see the variable name, here e1, drag the left edge of the dialog box to make it larger.] Place this table into the Word document.

2) Using SPSS, make a frequency bar chart of the variable e1 and place it into the document. Moving Tables and Charts into a Word Document:

1) Open a Word document.2) In SPSS right click on the table/chart to copy. Select the COPY AS option. From the dialog box that opens, select

EMF (enhanced metafile format).3) Move to the Word document and select Paste Special > Picture (enhanced metafile). [Note: Picture (jpeg) and

Bitmap options also seem to work.]a. To reduce the size of the table/chart, click on it, move the cursor to one of the corners, and drag towards the

center.b. To move the table/chart to any location, double click on it. From the top menu select the “Wrap Text” item

and then “tight.” [also found on the Page Layout Menu > Wrap Text]Analysis of the statistical output:

Below the table and chart, type a paragraph discussing the table that contains 1) an introductory statement; 2) a minimum of two descriptive statements ; and 3) a concluding statement. When discussing the contents of a table/chart/graph

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remember to use the statistics rather than just words such as “more” and “majority.” Incorporate statistics into your written presentation.

STAT 101

TOPICS: Sampling, Combinations & PermutationsDOCUMENTS

HANDOUTS: Green #4; Yellow #4 AVAILABLE ONLINE: Green #4; Yellow #4; Combinations ppt.; Qualitative

ppt.; Related Anatomy Sheets: Anatomy of a Systematic Random SampleASSIGNMENTS:

Text Readings: none Text Problems: none Problems on Yellow #3 (Sampling) & #4 (Combinations) Review Writing Descriptive Statements (located below) Items below

Next Class: TOPICS: Qualitative Data; DUE: QUIZ #1 (terms & sampling: see example #1 quizzes online)Stat Essentials (taken from today): Be able to: Sampling: identify sampling approaches; Combinations etc.:1) determine the number of samples via combinations; 2) calculating permutations, tree diagrams and the multiplication rule for independent events; Qualitative Data: 1) basics of qualitative data analysis (maybe).

COMBINATIONS & PERMUTATIONS on the TI Calculator: Math > Prob > select P or C, input the n and r values > enter; Factorials: enter the number, then go to Math > Prob > !

Writing Descriptive Statements:

Descriptive statements merely report data presented in a table, a graph/chart, or a statistic, such as the mean. To write a paragraph about a table: 1) introduce the table; 2) provide sentences describing some aspect of the data; and 3) write a summary sentence.

Example using the table to the right.[1) Introduction=>] The table to the right presents residents’ ratings of life in the village. [2) Descriptives=>] Approximately 78% of surveyed residents rated life in the village positively (good to excellent). In contrast, 77 of 347 residents (22.2%) rated life in the village as poor to fair. One hundred Eighty-three residents (52.7%) rated the quality of life as “good.”[3) Conclusion=>] In general, it would appear that most residents (77.8%) are satisfied with the quality of life in the village.

NOTES: The Rating of Quality table is a SPSS generated table. 1) Use the VALID PERCENT column for percentages. DO NOT use the “Percent” column as it includes missing data. 2) If you use words such as most, more than, fewer, approximately, etc., you MUST include supporting statistical evidence. Example: “Most residents rated life in the village as good.” How much is “most,” 30%, 80%? In contrast, “Most residents (52.7%) rated life in the village as good,” provides the reader with context for the descriptive statement.3) If you include numbers representing counts, also include the associated percentage value (e.g. “Eight respondents (15%) liked the movie.”). It is much easier for a reader to understand 15% than to have to figure out what 8 of 53 represents (15%).4) If you start a sentence with a number, as done above in the third descriptive statement, write it out (e.g. NOT “7 respondents liked …,” but rather “Seven respondents liked …” Additionally, the numbers one (1) through ten (10) are generally written out within sentences; others may be displayed numerically.

Problem 4.1: Write a paragraph containing: a sentence introducing the table; two sentences that contain descriptive statements resulting from the table’s content; and a conclusion you can draw from these data.

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Rating of qual i ty of l i fe in vi l lage

4 1.1 1.2 1.283 23.1 23.9 25.1

183 50.8 52.7 77.860 16.7 17.3 95.117 4.7 4.9 100.0

347 96.4 100.013 3.6

360 100.0

ExcellentVery GoodGoodFairPoorTotal

Valid

SystemMissingTotal

Frequency Percent Valid PercentCumulat ivePercent

6

Problem 4.2: Identify the variables and their characteristics:1: The number of doctors who wash their hands between patient visits.2: The majors of randomly selected students at a university.3: The average weight of mature German Shepherds.4: The category which best describes how frequently a person eats chocolate: Frequently, Occasionally, Seldom, Never.5: The temperature this morning at 7:00 a.m.6: The diameter of major league baseballs.7: The average horsepower of ten randomly selected 1.6L MINI Cooper engines.

Data Source* Variable Qual/Quant Discrete/Cont Nom/Ord/Int/Ratio

1: __________ _______________ __________ __________ __________

2: __________ _______________ __________ __________ __________

3: __________ _______________ __________ __________ __________

4: __________ _______________ __________ __________ __________

5: __________ _______________ __________ __________ __________

6: __________ ______________ __________ __________ __________

7: __________ ______________ __________ __________ __________*NOTE: Data Source is the population or sample unit from which you obtain the data, not the variable information (data) collected.

Problem 4.3: The Tax Man Cometh: The Internal Revenue Service wants to sample 1000 tax returns that were submitted last year to determine the percentage of returns that had a refund. Identify a sampling method that would be appropriate in this situation.

Problem 4.4: Prescription Drug Program: The director of a hospital pharmacy chooses at random 100 people age 60 or older from each of three surrounding counties to ask their opinion of a new prescription drug program. Identify the type of sampling used.

Problem 4.5: Combinations & PermutationsIce Cream: Thirty-one ice cream flavors > three scoops (different flavors) & a banana = one banana split. A) If the order of the flavors did not matter, how many different combinations of ice cream flavors could be made into a banana split? B) How many different ways could a banana split be made if order matters?

Permutation Calculation Combination Calculation

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STAT 101

TOPICS: Combinations; Qualitative DataDOCUMENTS

HANDOUTS: Green Sheet #5; Yellow #5 AVAILABLE ONLINE: Green #5; Yellow #5; PowerPoints: Qualitative Data,

Contingency Tables; Anatomy of Statistics for Qualitative Data, Pie, Bar, and Pareto ChartsASSIGNMENTS:

Text Readings - p. 10 (Qualitative data); 14 (pie bar charts)56-57 (pie & pareto charts) Text Problems – none – see yellow #4 & 5 EX#2 (optional) – online (please print out and submit) Items below.

FORMULAS: Multiplication Rule for Independent Events: k1 *k2 *k3∗. .. *kn-1 *kn [read as: event 1* event 2 * etc.]

Permutations: n Pr=

n!(n−r ) ! Combinations:

n C r=n!

(n−r )! r ! Both where n = number of items and r = number of items being used

Next Class: TOPICS: Qualitative Data; Contingency Tables (?); DUE: EX#2Stat Essentials (taken from today): Be able to: Combinations etc.:1) determine the number of samples via combinations; 2) calculating permutations, tree diagrams and the multiplication rule for independent events; Qualitative Data: 1) build qualitative tables; 2) build qualitative charts: pie, bar, pareto.

Problem 5.1: Combinations & PermutationsCoca Cola Directors: There are 11 members on the board of directors for the Coca Cola Company. A) If they must elect a chairperson, first vice president, second vice president; and secretary, how many different slates of four candidates are possible? B) If they must form a four-member ethics committee, how many different committees are possible?

Permutation Calculation Combination Calculation

Problem 5.2:In 2005 a television advertisement for Allstate Auto Insurance noted that last year (2004) 1.3 million people switched to Allstate. What is missing here?

Problem 5.3:Permutations & Combinations: You have ten paintings to hang, but only space to hang three. A) How many different ways could these paintings be hung if order matters? B) If order didn’t matter, how many different groups of three paintings could occur?

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Problem 5.4:Village Life: Identify the variable characteristics below.

Variable:

Qual or Quant: Measurement Level:

Write a brief paragraph regarding the information in this table.(See how to write a paragraph on sheet #4.)

Problem 5.5:Cell Phones:

Variable: Cell Phone Satisfaction Characteristics are: Categorical/Quant Discrete/Continuous/Neither N/O/I/R

Values: 1 = Fair; 2 = Good; 3 = Very Good; 4 = ExcellentData (n=31): 1,2, 3, 3, 3, 2, 2, 3, 3, 4, 3, 1, 3, 1, 3, 3, 3, 2, 2, 4, 3, 3, 3, 2, 2, 4, 4, 3, 3, 3, 3

Task 1: Build a qualitative frequency table of the variable Cell Phone. Include a table title, the variable values, frequencies, relative frequencies, cumulative frequencies, and cumulative relative frequencies.

Task 2: Build a Bar Chart of the variable Anxiety Level. Task 3: Build a Pie Chart of the variable Anxiety Level. Task 4: Build a Pareto Chart of the variable Anxiety Level. Task5: Write a paragraph that introduces the tables & charts, two sentences that describe information contained

within the frequency table, and a summary statement.

Rating of qual i ty of l i fe in vi l lage

4 1.1 1.2 1.283 23.1 23.9 25.1

183 50.8 52.7 77.860 16.7 17.3 95.117 4.7 4.9 100.0

347 96.4 100.013 3.6

360 100.0

ExcellentVery GoodGoodFairPoorTotal

Valid

SystemMissingTotal

Frequency Percent Valid PercentCumulat ivePercent

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STAT 101

TOPICS: Qualitative Data (practice); Contingency tables

DOCUMENTS HANDOUTS: Green Sheet #6; Yellow #6; Contingency Tables Reference; CA#1 AVAILABLE ONLINE: Green #6; Yellow #6; CA#1; Contingency Table and Quantitative PowerPoints; Anatomy

Sheets (5): Contingency tables; Quantitative Frequency Table; Histogram; Dot Plot; Stem-and-Leaf.HWK:

Text Readings - none Text Problems: none Yellow #5 & #6 problems not used in class CA#1 Items below

Next Class: TOPICS: Quantitative Data: Tables & Charts; DUE: CA#1Stat Essentials (taken from today): Be able to: QUALITATIVE: 1) calculate relative frequency, cumulative frequency, and cumulative relative frequency for response values; 2) build appropriate tables and charts; CONTINGENCY TABLES: 1) build tables; 2) interpret them.

Problem 6.1:Contingency Tables – Random Acts of Kindness: On day two of this course I asked members of three classes to respond to the following three questions.

1) If you could, would you tell someone the time if you were asked?2) A woman in front of you stumbles and drops her groceries. What would you do?3) A stranger walks up to you and asks to borrow your cell phone so that she can notify a friend where to meet her. Would you loan the phone?

Contingency tables can be used to break the data into sub-groups, thereby providing more information about who, in this case, would perform a random act of kindness. Create a contingency table for each of these three questions by sex and include column percentages.

1) Time by Sex 2) Groceries by Sex The Data:3) Phone by Sex

Consider: Which is the column variable and the row variable

and why? What is the size of each table? What happens to cases where one or both variables are

not available? Once built, do you see a trend within each table data? Do you see a trend across the three tables?

Problem 6.2:

COLOR TYPE STATUS GENDER MAKE ORIGINPurple Four-Door Commuter F DODGE AmericanPurple Four-Door Commuter F BUICK AmericanPurple Four-Door Commuter F CHRYSLER AmericanPurple Four-Door Commuter M SATURN AmericanPurple Four-Door Commuter M HONDA AsianPurple Four-Door Commuter F CHEVROLET AmericanPurple Four-Door Commuter F CHEVROLET AmericanPurple Four-Door Commuter F DODGE AmericanPurple Four-Door Commuter F DODGE AmericanPurple Four-Door Commuter F CHRYSLER AmericanPurple Four-Door Commuter F MERCURY AmericanPurple Four-Door Commuter F CHEVROLET AmericanPurple Suburban Commuter M SATURN AmericanPurple Two-Door Commuter F DODGE AmericanPurple Two-Door Commuter F CHEVROLET AmericanPurple Four-Door Commuter F HONDA AsianPurple Four-Door Commuter F PLYMOUTH AmericanPurple Four-Door Commuter F FORD AmericanPurple Four-Door Commuter F DODGE AmericanPurple Two-Door Commuter M ACURA AsianPurple Suburban Faculty M CHEVROLET AmericanPurple Suburban Faculty F DODGE AmericanPurple Two-Door Faculty M VOLKSWAGEN EuropeanPurple Two-Door Resident F CHEVROLET AmericanPurple Four-Door Resident M FORD AmericanPurple Two-Door Resident F CHEVROLET AmericanPurple Two-Door Resident M VOLKSWAGEN AmericanPurple Four-Door Resident M OLDSMOBILE AmericanPurple Four-Door Resident M SATURN AmericanPurple Four-Door Resident F PONTIAC AmericanPurple Four-Door Resident M PLYMOUTH AmericanPurple Four-Door Resident F TOYOTA AsianPurple Suburban Resident M MERCURY AmericanPurple Two-Door Resident M ACURA AsianPurple Four-Door Staff M HONDA AsianPurple Four-Door Staff F TOYOTA AsianPurple Pickup Truck Staff M DODGE AmericanPurple Suburban Staff F PLYMOUTH AmericanPurple Van Staff F PLYMOUTH American

Random Acts of Kindness Fall 2018

Time: Females - Yes 55; No = 0Time: Males - Yes 31, No 0Groceries: Females - Help 53, Not Help 2Groceries: Males Help 31; Not Help 0Phone: Females - Loan 31; Not Loan 24 Phone: Males - Loan 26; Not Loan 5

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Contingency Table – Purple Car People: During a past semester there were 39 purple cars registered on campus. Really?! Who owned these cars and what types of purple cars are various registrants driving? Contingency tables can be used to break the data into sub-groups, thereby providing more information about who, in this case, owns purple cars.Create a contingency table that crosses vehicle Type with Status. Which variable should be the column variable and which the row variable?

Consider: Which is the column variable and why? What is the size of this table? Once built, do you see a trend within the data?

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STAT 101

TOPICS: Quantitative Data Tables, Charts & GraphsDOCUMENTS

HANDOUTS: Green #7; Yellow #7 (Quantitative Data) AVAILABLE ONLINE:

o Green #7; Yellow #7; o PowerPoint (2): Quantitative Data; Frequency Polygons & Ogives; o Anatomy Sheets (4): Quantitative Frequency Table; Histogram, Dot Plot, Stem-and-Leaf;

HWK: Text Read: Ch. 2 sections 2.1, 2.2 (covered over next couple classes). Text Problems: none: work contingency table and quantitative table problems on green & yellow sheets.) Items below.

Next Class: TOPICS: Quantitative Data – Charts (cont.)Stat Essentials (taken from today): Be able to: CONTINGENCY TABLES: 1) build tables; 2) interpret them; QUANTITATIVE TABLES: 1) build a frequency table appropriate for the presentation of quantitative data; 2) identify frequency table components – classes, boundaries, etc.; and it we get there, 3) build charts/graphs appropriate to quantitative data – histogram, dot plot, stem-and-leaf, frequency polygon, ogive (won’t get to all today).

Problem 7.1: Contingency Tables: Using the table below, find the requested percentages or counts. The data present three cities in which houses were sold and during which month the houses sold.

What is the size of this contingency table? ____ by ____

Among houses sold in Arlington, what percent were sold in June and July?

During August _____% of the houses were sold in Fort Worth.

Among all houses _____% were sold in Dallas during September.

Looking at the right marginal totals column what does the 131 value represent?

T or F: Thirty percent of the houses sold in June were sold in Dallas.

T or F: Thirty-two percent of the houses were sold in Fort Worth.

T or F: Of the houses sold in July, approximately 25% were sold in Dallas.

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Problem 7.2: Obtaining statistical output and providing analysisIdeal Weight: Twenty five students reported their ideal weights (in most cases, not their current weight). Weights (lb): 110 115 123 130 105 119 130 125 120 115 120 120

120 110 120 150 110 130 120 118 120 135 130 135110

Create a frequency table containing five classesWrite a paragraph containing an introduction and a minimum of two descriptive statements.

Identify:Midpoint of the third class: ___________ Boundaries of the first class; ____________

Class limits of the second class: ___________ Width of the classes: ____________

Based upon your table make the following charts/graphs (NOTE: do only those demonstrated today): histogram, dot plot, stem-and-leaf, frequency polygon, ogive.

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STAT 101

TOPICS: Quantitative Tables & Charts (cont.)DOCUMENTS:

HANDOUTS: Green #8 AVAILABLE ONLINE: Green #8; PowerPoints (4): 1) Distribution Shapes; 2) Sigma; 3)

Quantitative Data; 4) Quantitative Charts - Freq. Polygon, Ogive, Line Chart ppt. ANATOMY REFERENCE SHEETS: various charts for quantitative data

HWK: Text Reading: Ch. 2, review sections 2.1-2.2 – graphs & charts Text Problems: beginning on p. 125 #1, 8, 10, 12, 18a (also a histogram, and an ogive for #18); p. 139 # 74 (Stem-&-

Leaf and a Dot Plot) CA#2 (due Tuesday) QUIZ #2: potential topics: combinations & permutations; reading tables and charts Items below

Next Class: TOPICS: Distribution shapes; SIGMA); Measures of Center (?); QUIZ #2 DUE: CA#2

Stat Essentials (as with prior class): Be able to: 1) build a frequency table appropriate for the presentation of quantitative data; 2) identify frequency table components – classes, boundaries, etc.; 3) build charts/graphs appropriate to quantitative data – histogram, dot plot, stem-and-leaf, frequency polygon, ogive.

Problem 8.1: Nutrition Bars: (NOTE: Assume Lower Class Limits are shown)

How many values are in the data set?

How many classes are there?

What is the width of a class?

How many milligrams of sodium are in the nutrition bar with the highest value?

Explain how a relative frequency histogram would differ from the displayed chart. (Hint: Think about how frequency and relative frequency bar charts differ?)

Problem 8.2: Contingency Tables: Using the contingency table, find the requested percentages or counts. The data present the opinions of students regarding ecological disaster possibilities based upon their geographic origin.

What is the size of this contingency table? ____ by ____

Among students from urban areas, what percent strongly agreed?

For Unsure respondents, _____% were from Rural areas.

Among all respondents, _____% were from Urban Clusters.

Looking at the right marginal totals column what does the 30 value represent?

Respondents who were from Urban areas and Mildly Disagree with the statement represent what percent of all respondents?

T or F: Sixty percent of the respondents were from a Rural area and indicated a Mildly Agree response.

T or F: Approximately 17% of respondents were from Urban areas.

T or F: Of the respondents selecting Strongly Agree, approximately 33% were from Rural areas.

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Problem 8.3: Retirement Ages: (Larson & Farber p. 51 #39)Using the following data, build both a single stem and a double stem, stem-and-leaf.

Ages: 70 54 55 71 57 58 63 65 60 66 57 62 63 60 63 60 66 60 67 69 69 52 61 73

Problem 8.4: Retirement Ages: Using the data from problem 8.3, build a frequency table containing five classes. [NOTE: Without a stated starting point, make sure that the minimum value fits into the first class and the maximum value is within the fifth class. If the latter does not occur, either shift the starting point of the first class, while maintaining class width, or increase the size of the class width.]

Problem 8.5: Balance: Eyes closed average of two trials (seconds): Right foot: _____Left foot: _____ One of the leading health concerns for people over 60 is falling. Balance in walking and standing is dependent on many factors. (www.vestibular.org)

As people grow older, they may have difficulty with their balance. Roughly 9 percent of adults who are 65 and older report having problems with balance. Having good balance means being able to control and maintain your body's position, whether you are moving or remaining still. An intact sense of balance helps you: walk without staggering; get up from a chair without falling; climb stairs without tripping. Balance disorders are one reason older people fall. According to the Centers for Disease Control and Prevention, more than one-third of adults ages 65 years and older fall each year. Among older adults, falls are the leading cause of injury deaths. (nihseniorhealth.gov)

Aging and balance-good news, bad news Running & FitNews,  April, 2002  Here's the bad news. Along with the visible signs of aging, and the obvious declines in the cardiovascular, respiratory, and orthopedic systems, your body is slowly assembling a collection of deficits that significantly reduce your ability to maintain balance. A decrease in balance ability, if nothing else, can increase your risk of acute running injuries such as sprains and falls.

Balance is a matter of collecting information from the environment on where your body is in space and how its position is changing, and then responding with adjustments by your musculoskeletal system. Age-related changes occur in the sensory, motor, cognitive, and musculoskeletal systems, all affecting your ability to perceive and process the necessary environmental cues, and to respond quickly and efficiently to the information. Visual acuity, depth perception, contrast sensitivity, and peripheral vision decline with age and these changes reduce or alter the environmental data your brain uses to maintain balance. Meanwhile, your sensitivity to tactile messages, such as vibration and sensory input from the soles of your feet, is also declining, causing you to rely more on your decreased visual abilities. At the same time, the tiny hair cells within the vestibular system are becoming less sensitive to head motion, diminishing the response of the ocular reflex that stabilizes your eyes. These balance deficits are probably the main reason you will almost never see individuals beyond 60 or so, riding a roller coaster for fun.

There is good news, however. First of all, runners and other athletic individuals probably suffer these declines more slowly than their sedentary contemporaries. Even better, there is still more you can do to slow declines in balance ability. To test your balance, try standing on one leg with your arms folded over the raised leg, knee tucked toward your chest, for 30 seconds. You should be able to do this without dropping the raised leg or hopping around. Next, if you felt reasonably stable on one leg, try 30 seconds with your eyes closed. Now try standing on both feet, with one foot directly in front of the other, heel touching toes. Repeat with your eyes closed. If nothing else, you will learn just how important visual cues are in maintaining balance. Exercises that challenge the multiple systems your body uses for balance, such as the two tests above, can slow age-related declines and even improve balance significantly, whatever your starting point.

One of the very best things you can do to improve and maintain balance is to use free weights for strength training. Lifting free weights requires attention to posture and form, while core-stabilizing muscles continuously adjust to the motion of the weights. Using a balance ball instead of a bench while lifting free weights, or standing on an unstable surface such as a balance board, further stimulates and challenges your balance.

Include balance training in your fitness plan along with the training of the cardiovascular, musculoskeletal, and respiratory systems you get from running. It's one of the best things you can do to slow the aging process. For information on more balance exercises, go to http://gymball.com/balance_exercises.html. (Biomechanics, 2001, Vol. 8, No. 11, pp. 79-86); COPYRIGHT 2002 American Running & Fitness Association; COPYRIGHT 2003 Gale Group. Source: findarticles.com

15

STAT 101:

TOPICS: Quantitative Tables & Charts (practice) DOCUMENTS:

HANDOUTS: Green #9 AVAILABLE ONLINE: Green #9; PowerPoints for: 1) Sigma, 2) Measures of Center; 3)

Distributions, 4) Time Series Charts (in with Freq. Polygon & Ogive); Anatomy sheets: Sigma

ASSIGNMENTS: Text Readings: Ch. 2, sections 2.5 – 2.7 (in preparation for next class) Text Problems: none Items below – build tables not made by your work group and try a couple of charts

NEXT CLASS: Distribution Shapes; Time Series Charts; SIGMA); Measures of Center & Variation (?)Stat Essentials (taken from today): Be able to: Build Quantitative tables & charts - practice session.

IN-CLASS ASSIGNMENT: Using the data provided for your problem complete the following: Create a grouped frequency table according to the instructions specific to your problem. Create at a minimum the chart assigned to your work group – others if you have time. Present your chart on one of the white boards.

GROUPS LISTED IN RED: PROBLEM SET #1 - RADIATION IN BABY TEETHListed below are the amounts of strontium-90 (in millibecquerels or mBq) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based upon data from “An Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990’s” by Mangano, et al., Science of the Total Environment). Frequency Table: class width = 10; midpoint of first class = 114.5

GROUPS LISTED IN BLACK: PROBLEM SET #2 - SETTING SPEED LIMITSListed below are recorded speeds (in miles/hour: mph) of randomly selected cars traveling on a section of Highway 405 in Los Angeles (based upon data from Sigalert). That section has a posted speed limit of 65mph. Traffic engineers often establish speed limits by using the “85th percentile rule,” whereby the speed limit is set so that 85% of drivers are at or below the speed limit. Frequency Table: class width = 3; midpoint of first class = 56

GROUPS LISTED IN BLUE: PROBLEM Set #3 - TRADE WINDSTrade winds are one of the beautiful features of island life in Hawaii. The following data represent total air movement in miles each day over a weather station in Hawaii as determined by a continuous anemometer recorder. The period of observation was January 1 to February 15, 1971. Frequency Table: class width = 20; midpoint of first class = 9.5

99.24.19

16

STAT 101:

TOPICS: Distribution Shapes; Time Series Charts; Σ (Sigma); Measures of Center DOCUMENTS:

HANDOUTS: Green #10; Yellow #9 AVAILABLE ONLINE: Green #10; Yellow #9; PowerPoints for: 1) Sigma, 2) Measures of

Center; 3) Distributions, 4) Time Series Charts (in with Freq. Polygon & Ogive); Anatomy sheets: Sigma

ASSIGNMENTS: Text Readings: Ch. 2, sections 2.5-2.7 Text Problems: Dot Plot and S&L p.125 #2; Hist. use data p. 129 #18b; Freq. Polygon p. 130 #20; Time Series p. 131

#22; using the data about trees (p. 125 #2) build a frequency table containing five classes given an upper boundary of one class a t30.5.

Finish Yellow #9 sigma problems – you have to know how to do this. Items below

NEXT CLASS: Measures of Center (cont.), Variation, and Position (?) DUE: EX#3SStat Essentials (taken from today): Be able to: DISTRIBUTIONS: 1) identify distribution shapes and characteristics; TIME SERIES: 1) create time series chars (line charts) given two variables; SIGMA: 1) understand what the symbol (Sigma) means; 2) successfully demonstrate the application of MEASURES OF CENTER 1) calculate an arithmetic mean, median, mode; 2) identify when you would use each of these measures.

Problem 9.1:An introductory statistics class had three exams, for which the grade distribution of each exam is presented to the right. For each exam describe the distribution’s shape and comment on the exam’s difficulty. [Consider the x-axis point C1 to be the exam’s mean grade.]

Distribution Shape Difficulty of Exam (easy, average, hard)

Exam #1: _________________ _________________

Exam #2: _________________ _________________

Exam #3: _________________ _________________

Problem 9.2:SIGMA: Given the following data for X and Y, determine the values of Sxx and Syy.

X Y S xx=Σx 2

−(Σx )2

n S yy=Σy 2

−(Σy )2

n =

20 4

38 10

10 2

68 8

104 28

87 23

109.26.19

17

Problem 9.3:SIGMA: Given the following data for X and Y, determine the values of r. [Note: same data as in problem 9.2.]

X Y r= nΣ xy−(Σx)(Σy )

√ [nΣx2−(Σx )2 ] [nΣy2−(Σy )2 ]=

20 4

38 10

10 2

68 8

104 28

87 23

Problem 9.4Time Series: Create a time series chart of the Murder Rates in New York City

Problem 9.5Build a complete frequency table of 25 tree heights (ft.) that contains five classes with an upper boundary of one class at 36.5. (text data ,p. 125 #2)

Tree heights: 25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54

Murder Rates in NYC*Year Rate1990 14.51991 14.21992 13.21993 13.31994 11.11995 8.51996 7.41997 6.01998 5.11999 5.02000 5.02001 5.02002 4.82003 4.92004 4.62005 4.52006 4.82007 4.22008 4.32009 4.02010 4.52011 3.92012 3.52013 3.02014 2.7

*per hundred thousand

18

STAT 101

TOPICS: Measures of Center & VariationDOCUMENTS:

HANDOUTS: Green sheet #11; Yellow #111 AVAILABLE ONLINE: Green #11; Yellow #11; PowerPoint:

Measures of Center, Measures of Variation, Measures of Position.ASSIGNMENTS:

Text Review: Ch. 2 Review 2.5-2.7; Read 2.3-2.4 Text Problems: Center: p. 134 #43-45 (data on p. 133 – boat

lengths); Dist. Shapes: p. 134 #52-58; Variation: p. 133 (boat length data) determine – range and standard deviation (use s.d. computational formula)

Extra Credit #3 Items below

FORMULAS (For Samples): Mean Variance Standard Deviation

Definition formula): x=∑i=1

n

x i

ns2=

Σ( x−x¿)2

n−1 s=√∑( x− x )2

n−1

Computational formula): aboves2=

nΣx2−(Σx )2

n(n−1) s=√ n∑ x2−(Σx)2

n (n−1 )Median: 1) middle score if odd number of values; 2) mid-point between two middle scores if even number of valuesMode: most frequent value (multiple modes may exist); represents the center of qualitative data

Midrange: minimum+maximum

2NEXT CLASS: TOPIC: Measures of Variation (cont.) & Position DUE: EX#3 (optional)Stat Essentials (taken from today): MEASURES OF CENTER: Be able to: 1) calculate an arithmetic mean, median, mode; 2) identify when you would use each of these measures; MEASURES OF VARIATON: Be able to:1) explain what a standard deviation represents; 2) obtain a standard deviation using either formula (definition or computational); 3) interpret what the standard deviation represents in a given situation; 4) Empirical Rule;.5) Chebychev’s Theorem.

Problem 11.1:Blood Pressure: Given the following sample of systolic blood pressures, determine their mean, median, mode, and midrange; using the COMPUTATIONAL FORMULAS, determine the variance and standard deviation for this variable.

Systolic Pressures: 120 145 86 133 115 124 153 98 144 132

1110.1.19

NOTICE: MID-TERM EXAM IS SCHEDULED FOR OCTOBER 10. PLAN ANY TRAVEL ARRANGEMENTS TO ACCOMMODATE THIS EVENT.

19

Problem 11.2 CRICKETS:

THE DATA: Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (Fahrenheit) and the number of chips per second for the striped ground cricket.

X: Temperature (Fo): 69.4 69.7 71.6 75.2 76.3 79.6 80.6 80.6 82.0 82.6 83.3 83.5 84.3 88.6 93.3Y: Chirps/second: 15.4 14.7 16.0 15.5 14.4 15.0 17.1 16.0 17.1 17.2 16.2 17.0 18.4 20.0 19.8

1) Measures of Center: Determine the mean, median, mode, and midrange for both variables.2) Measures of Variation: Determine the range, variance and standard deviation for both variables.

Problem 11.3Cricket frequency table: Using the temperature data from problem 11.2, build a frequency table containing five classes where the midpoint of one class is located at 76 degrees. Build a stem & leaf and dot plot of these data.

20

STAT 101

NOTICE: ANYONE SEEKING TO TAKE THE MID-TERM EXAM AT ACCESSIBILITY RESOURCES, MUST COMPLETE A REQUEST TO DO SO ONLINE.

TOPICS: Measures of Variation & Position; Box plots; z-score; Pearson’s I, Coefficient of Variability (CVAR)DOCUMENTS:

HANDOUTS: Green #13; Yellow #13 AVAILABLE ONLINE: Green #13; Yellow #13; PowerPoints: Measures of Position

HWK: Text Readings: Review suggested readings to date Text Problems: Text problems not attempted to date CA#3 (distributed and available online) Items below

FORMULAS: Mean, median, quartiles, variance, standard deviation on prior sheets

Q1=n+1

4 Q2=n+1

2 Q3=3(n+1)

4 IQR=Q3−Q1

LowerLimit=Q1−1. 5( IQR) UpperLimit=Q3+1. 5( IQR)

z-score: z= x−μ

σ Pearson’s I=3( x−median )

sCVAR= s

x¿ ∗100 %

NEXT CLASS: Exam Review DUE: CA#3Stat Essentials (taken from today): MEASURES OF POSITION: Be able to: 1) obtain the five-number-summary; If we get there:2) build a box plot; 3) determine variability measures: skew (Pearson’s I), Coefficient of Variability, z-score.

Exam 1 Topic Areas for Review:See Handouts distributed through today. This is a comprehensive, cumulative exam.Potential exam topics:1. terms and their relationships 2. assessing table & chart content for accuracy3. interpretation & discussion of table & chart content 4. recognition of appropriate/inappropriate data presentation5. sampling techniques – identification 6. combinations, permutations, multiplication rule for independent events, tree diagrams 7. building qualitative tables and charts (pie, pareto, bar)8. building quantitative tables (2 types) and charts (histogram, dot plot, stem-and-leaf, ogive; freq. polygon, time series)9. Distribution shapes, Pearson’s Index of Skewness10. SIGMA11. measures of center: mean, median, mode, midrange12. measures of variation: range, standard deviation, inter-quartile range (Q3 –Q1)13. Empirical Rule & Chebychev’s Theorem14. measures of position: minimum, Q3, Q2, Q1, maximum, z-score, CVAR, Box Plots w/ related values (limits, IQR, adjacent point(s))

Exam 1 Review Materials:1. Green sheets & answer key2. Yellow sheets & answer keys3. Anatomy of Statistics sheets (online)4. Sample Exams (online)5. Course Review Materials (online)6. In-class review problems (next class)7. Text book8. ME – stop in or make an appointment (T & Th: 8-8:20; 11:20-12; 1:30-2:20; 4:00 –

5:00; W: afternoons - set a time)9. Must be something else…

1210.3.19

Know these value ranges:Standard Deviation: 0 to ∞ [Note: you cannot get a negative std. dev.]Probability: 0 to 1, inclusive

21

CRICKETS:

THE DATA: Temperature vs. Cricket Chirps: Crickets make a chirping noise by sliding their wings over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (Fahrenheit) and the number of chips per second for the striped ground cricket.

X: Temperature (Fo): 69.4 69.7 71.6 75.2 76.3 79.6 80.6 80.6 82.0 82.6 83.3 83.5 84.3 88.6 93.3Y: Chirps/second: 15.4 14.7 16.0 15.5 14.4 15.0 17.1 16.0 17.1 17.2 16.2 17.0 18.4 20.0 19.8 Given: xxyyxy

REFER TO Green #11 FOR YOUR ANSWERS TO THE FOLLOWING: Determine the mean, median, mode for both of these variables. Using the computational formula, determine the standard deviations for these two variables.

Problem 12.1: SkewDetermine, using Pearson’s I, whether or not the variables are skewed.

Temperature I: _____ Chirps I: _____

Yes No (circle one): Given the value of “I,” we would consider this variable approximately normally distributed.

Temperature: Yes No Chirps: Yes No

Problem 12.2: z-scoreFor the variable’s maximum value, determine how many standard deviations it is away from the mean.

Temperature z = _____ Chirps z: _____

Problem 12.3: VariabilityDetermine the variability of the variable.

Temperature CVAR = _____ Chirps CVAR: _____

As a result of comparing variability via CVAR, it appears that ______________ has greater variability than ___________.

Problem 12.4: Box plotsCreate a modified box plot for each variable. Although you may not need these values, calculate the IQR, upper limit, and lower limit.

Temperature: All Measures in: _______ Min: ____ Q1: ____ Q2: ____ Q3: ____ MAX: ____

IQR: ____ L. Limit: ____ U. Limit: ____ Adj. Pt. (if any): ____

Chirps: All Measures in: _______ Min: ____ Q1: ____ Q2: ____ Q3: ____ MAX: ____

IQR: ____ L. Limit: ____ U. Limit: ____ Adj. Pt. (if any): ____

Temperature Box Plot Here (use line as the x-axis) Chirps Box Plot Here (use line as the x-axis)

_______________________________________ _________________________________________

22

23

STAT 101

TOPICS: Mid-Term review SessionDOCUMENTS:

HANDOUTS: Green #13; Yellow #13 (review sheet); MID-TERM EXAM Take-Home Problems

AVAILABLE ONLINE: Green #13; Yellow #13 HWK:

Text Readings: Review prior green sheets for sections. Text Problems: Review prior green sheets for problems. Items below

FORMULAS TO DATE :

Combination/Permutations/etc.: Permutations: n Pr=

n!(n−r )! Combinations:

n C r=n!

(n−r )! r ! Both where n = number of items and r = number of items being used

Multiplication Rule for Independent Events: k1 *k2*k3∗. .. *kn-1 *kn [read as: event 1* event 2 * etc.]Measures of Center & Variation (computational formulas only):

Mean Variance Standard Deviation

Computational formula(s): x=∑i=1

n

x i

ns2=

nΣx2−(Σx )2

n(n−1) s=√ n∑ x2−(Σx)2

n (n−1 )Median: 1) middle score if odd number of values; 2) mid-point between two middle scores if even number of valuesMode: most frequent value (multiple modes may exist); represents the center of qualitative data

Midrange: minimum+maximum

2

Measures of Position:Q1=

n+14 Q2=

n+12 Q3=

3(n+1)4 IQR=Q3−Q1

LowerLimit=Q1−1. 5( IQR) UpperLimit=Q3+1.5( IQR)

NEXT CLASS: MID-TERM EXAM Stat Essentials (taken from today): Be able to: Address topics to date:

Exam 1 Topic Areas for Review:See Handouts distributed through today. This is a comprehensive, cumulative exam.Potential exam topics:1. terms and their relationships2. assessing table & chart content for accuracy3. interpretation & discussion of table & chart content 4. recognition of appropriate/inappropriate data presentation5. sampling techniques – identification 6. combinations, permutations, multiplication rule for independent events, tree diagrams 7. building qualitative tables and charts (pie, pareto, bar)8. building quantitative tables (2 types) and charts (histogram, dot plot, stem-and-leaf, ogive; freq. polygon, time series)9. Distribution shapes, Pearson’s Index of Skewness10. SIGMA11. measures of center: mean, median, mode, midrange12. measures of variation: range, standard deviation, inter-quartile range (Q3 –Q1)13. Empirical Rule & Chebychev’s Theorem14. measures of position: minimum, Q3, Q2, Q1, maximum, Box Plots w/ related values (limits, IQR, adjacent point(s))

Exam 1 Review Materials:1. Green sheets & answer key2. Yellow sheets & answer keys3. Anatomy of Statistics sheets (online)4. Sample Exams (online)5. Course Review Materials (online)6. In-class review problems (next class)7. Text book & problems8. ME – stop in or make an appointment (T & Th: 8-8:20; 11:20-12; 1:30-2:20; 4:00 – 5:00; W: afternoons - set a time)

1310.8.19

24

9. Must be something else…

STAT 101

TOPICS: MID-TERM EXAMDOCUMENTS:

HANDOUTS: Green #14 AVAILABLE ONLINE: Green #14

ASSIGNMENTS: TAKE A BREAK AFTER YOU READ THIS (could be on the next quiz)

NEXT CLASS: TOPIC: Data collection for mid-term application lab assignment Stat Essentials (taken from today): To see what we know

Portion sizes increase in 'Last Supper' paintings (An application of statistics)By Nanci Hellmich, USA TODAY (3/23/2010)

If your food portions seem to have grown larger over the years, you have some blessed company.

Two researchers analyzed the food and plate sizes in 52 of the most famous paintings of The Last Supper and found that the portion sizes in the paintings have increased dramatically over the past millennium, from years 1000 to 2000.

Using a computer program, they compared the size of loaves of bread, main dishes and plates to the size of the heads of the disciples and Jesus in the artwork, including Leonardo da Vinci's famous depiction of the event.

Findings published in April's International Journal of Obesity: Over that 1,000-year period, the main course size increased by 69%, plate size 66% and loaves of bread 23%. The biggest increases in size came after 1500.

The researchers used paintings of this event "because it is the most famous supper in history," which artists have been painting for centuries, so the paintings provide information about plate and entree sizes over time, says Brian Wansink, director of the Cornell (University) Food and Brand Lab in Ithaca, N.Y. One possible reason for the increase: Food may have become more available and less expensive, he says.

He did the research with his brother, Craig, a professor of religious studies at Virginia Wesleyan College in Norfolk, and a Presbyterian minister.

The three Gospels (Matthew, Mark and Luke), which include descriptions of The Last Supper, mention only bread and wine, but many of the paintings have other foods, such as fish, lamb, pork and even eel, says Craig Wansink.

The use of fish in the meals is symbolic because it's an image that is used to represent Christianity, he says. Among the reasons for the symbolism: A number of the disciples were fishermen, and Jesus told them "to be fishers of men," he says. Plus, he says, Jesus performed several miracles with fishes and loaves.

As Easter approaches, he says, people may want to study the paintings because they illustrate one of the "most important moments in Christianity

ABOVE: "The Last Supper" painting by Duccio, 1308-11. Note the size of the food and drink on the table compared to the size of the heads of Jesus and his disciples.BELOW: "The Last Supper" painting by Tiziano Vecellio Titian.

1410.10.19

25

STAT 101 NAME: ________________________________________

TOPICS: Application Lab Data CollectionDOCUMENTS:

HANDOUTS: Green #15 AVAILABLE ONLINE: Green #15

ASSIGNMENT: Midterm Application Assignment Extra Credit #8 (NOTE: Response for this optional assignment must be submitted electronically by 11:59:59

Thursday October 17)NEXT CLASS: TOPIC: Measures of Position; Correlation DUE: Midterm Application Assignment Stat Essentials (taken from today): To see what we know.

RAK: enter 1 OR 2 for answer Hand Strength Hand Endurance Hand AgilityQ1 Q2 Q3 Right Left Right Left Time

RAK:

1) If you could, would you tell a person what time it was if you were asked? 1) Yes 2) No

2) A woman just in front of you stumbles and drops her groceries.

What would you do? 1) Stop and help pick up the items. 2) Ignore her and keep moving.

3) A stranger walks up to you and asks to borrow your cell phone so that she can notify a friend where to meet her.

Would you loan the phone? 1) Yes 2) No

Hand Strength:For each hand, determine your average hand strength (average of three trails).

MEASURE IN POUNDS: If you use the kg hand dynamometer, convert by multiplying result by 2.2 (1 kg = 2.2 lb).

Right hand average: __________ lb. Left hand average: __________ lb.

Hand Endurance:Squeeze a star as hard AND fast as you can until you can no longer complete the task.

TIME USING CELL PHONE TO TWO DECIMALS.

Right hand time: __________ sec. Left hand time: __________ sec.

Hand Agility:Start with a stack of six yogurt cups. Create a pyramid with the cups and return them to a stack of six as quickly as possible. Determine an average time for three trials (take a practice run before timing run).

TIME USING CELL PHONE TO TWO DECIMALS.

Stacking time: __________ sec.m&m’s

Total Blue Brown Green Orange Red Yellow

1510.17.19

26

27

STAT 101

TOPICS: Box plots; z-score; Pearson’s I, Coefficient of Variability (CVAR); CorrelationDOCUMENTS:

HANDOUTS: Green #16; Yellow #16; Table: Critical Values of Pearson Correlation Coefficient

AVAILABLE ONLINE: Green #16; Yellow #16; PowerPoints: Measures of Position, Correlation, RegressionHWK:

Text Readings: ch. 12 12.2 (scatter plots), p. 690 (correlation) Text Problems: p. 720 #60,61 EX#4 Items below

FORMULAS

z-score: z= x−μ

σ Pearson’s I=3( x−median )

sCVAR= s

x¿ ∗100 %

NEXT CLASS: Correlation & Regression; Quiz #3 [measures of position] DUE: EX#4Stat Essentials (taken from today): Be able to: Measures of Position: 1) build a box plot; 2) determine variability measures: skew (Pearson’s I), Coefficient of Variability (CVAR), z-score; If we get there, Correlation: 1) describe general steps leading to regression; 2) make a scatter plot; 3) calculate the Pearson Product Moment Correlation Coefficient, r.

Woodpeckers: Forest managers are increasingly concerned about the damage done to animal populations when forests are clear-cut. Woodpeckers are a valuable forest asset, both because they provide nest and roost holes for other animals and birds and because they prey on many forest insect pests. The article “Artificial Trees as a Cavity Substrate for Woodpeckers,” (Journal of Wildlife Management [1983]) reported on a study of how woodpeckers behaved when provided with polystyrene cylinders as an alternative roost and nest cavity substrate. Noted below are selected values of X = ambient temperature (Co) and Y = cavity depth (in centimeters). [Devore & Peck p. 558]

Observation: 1 2 3 4 5 6 7 8 9 10 11 12X: Temperature (Co): -6 -3 -2 1 6 10 11 19 21 23 25 26Y: Hole Depth (cm): 21.1 26.0 18.0 19.2 16.9 18.1 16.8 11.8 11.0 12.1 14.8 10.5

Given: n = 12 x = 131 y = 196.3 x2 = 2939 y2 = 3445.25 xy = 1622.3

Problem 16.1: Skew [Pearson’s I]Determine the skew of both variables.

Problem 16.2: z-score

1610.22.19

Statistics

N Valid

Missing

Mean

Median

Mode

Std. Deviation

Variance

Range

Minimum

Maximum

Percentiles 25

50

75

12 12

0 0

10.9167 16.3583

10.5000 16.8500

-6.00 a 10.50 a

11.71214 4.61331

137.174 21.283

32.00 15.50

-6.00 10.50

26.00 26.00

-1.2500 11.8750

10.5000 16.8500

22.5000 18.9250

a.

28

Determine the number off standard deviations the maximum value is from the mean.

Problem 16.3: Coefficient of VariabilityWhich variable is exhibiting greater variability?

Problem 16.4: Box plotBuild a modified box plot of hole depth.

Problem 16.4: ScatterplotGiven the following data, construct a scatterplot. [Larson 4ed p. 486]

X [Height (in)]: 68 72 65 70 62 75 78 64 68Y [Pulse/min]: 90 85 88 100 105 98 70 65 72

29

STAT 101

TOPICS: Correlation & Regression DOCUMENTS:

HANDOUTS: Green #17; CA#4 AVAILABLE ONLINE: Green #17; CA#4

HWK: Text Readings: CH. 12 sections 12.3 – 12.5 Text Problems: p. 720 #59; p. 724 #70 (DO ONLY parts a – c and e) CA#4 (15 pts.)

FORMULAS:Hypotheses: Null Hypothesis (H0) vs. Alternative Hypothesis (Ha) for correlations:

Statistically: In Words:

H0: ρ=0 (rho=0 ) H0: There is no linear relationship between variable X and variable Y.

Ha: ρ≠0 (rho≠0 ) Ha: There is a linear relationship between variable X and variable Y.

EXAMPLE (using the variables Height & Weight): H0: ρ=0 H0: There is no linear relationship between HEIGHT and WEIGHT. Ha: ρ≠0 Ha: There is a linear relationship between HEIGHT and WEIGHT.

Correlation:r= nΣ xy−(Σx )(Σy )

√nΣx2−(Σx )2√nΣy2−(Σy )2

Regression: [where b1 = slope and b0 = y-intercept]

y¿

=b0+b1 x b1=

nΣ xy−(Σx )(Σy)n (Σx2)−(Σx )2 b0= y−b1 x or

b0=(Σy )(Σx2 )−(Σx )(Σ xy )

n(Σx2 )−(Σx )2

NEXT CLASS: TOPICS: Correlation & Regression DUE: CA#4Stat Essentials (taken from today): 1) Be able to: 1) identify the steps leading to correlation and regression; 2) Scatter Plot – building and interpreting; 3) conduct a correlation by hand and via SPSS; 4) Read the Pearson’s Correlation Coefficient Table of Critical Values; 5) Basics of Regression.

Problem 17.1:Woodpeckers: Forest managers are increasingly concerned about the damage done to animal populations when forests are clear-cut. Woodpeckers are a valuable forest asset, both because they provide nest and roost holes for other animals and birds and because they prey on many forest insect pests. The article “Artificial Trees as a Cavity Substrate for Woodpeckers,” (Journal of Wildlife Management [1983]) reported on a study of how woodpeckers behaved when provided with polystyrene cylinders as an alternative roost and nest cavity substrate. Noted below are selected values of X = ambient temperature (Co) and Y = cavity depth (in centimeters). [Devore & Peck p. 558]

Observation: 1 2 3 4 5 6 7 8 9 10 11 12X: Temperature (Co): -6 -3 -2 1 6 10 11 19 21 23 25 26Y: Hole Depth (cm): 21.1 26.0 18.0 19.2 16.9 18.1 16.8 11.8 11.0 12.1 14.8 10.5

Given: n = 12 x = 131 y = 196.3 x2 = 2939 y2 = 3445.25 xy = 1622.3

1710.24.19

NOTE: Substitute the study’s variables in place of “variable X” and “variable Y.”

NOTE: Rho = 0 indicates there is no linear correlation.

Rho ≠ 0 indicates that there is a linear correlation.

30

1) What is being studied? Relationship between ____________________________________

2) Does it make sense to study a relationship between these two variables? _____

Why? ________________________________________________________________________

3) State in words the null and alternative correlation hypotheses to be tested.

H0: ρ=0 ___________________________________________________________

Ha: ρ≠0 ___________________________________________________________

4) Make a scatter plot of these variables.

5) If the scatter plot indicates a relationship between these two variables. Calculate the correlation for the two variables.

r = _________

6) Determine if the correlation is statistically significant (circle ONE): not sig. = .05 = .01(Use: Critical Values for the Pearson’s Correlation Coefficient Table; text page A26)

PROCEED??? Resulting from the statistical significance determination, the following options occur:If yes, go on to regression.

If no, regression should not be attempted and best estimate becomes the mean of the Y variable, y .

31

STAT 101

TOPICS: Correlation & RegressionDOCUMENTS:

HANDOUTS: Green #18 AVAILABLE ONLINE: Green #18; Normal Distribution ppt.

ASSIGNMENT: Text Readings: CH. 12 review sections 12.3 – 12.5; CH. 6 sections 6.1-6.2 (Normal Distribution) Text Problems: p. 724 #70 (parts d, f - i; already did a – c and e – right?) Extra Credit #5 Items below.

FORMULAS: Correlation & Regression formulas on prior sheetCoefficient of Determination, r2, = Correlation Coefficient, r, squared (r2) OR

r2=SSExplainedSSTotal =

r2=Σ( y¿̂− y−)2

Σ( y− y−

)2¿

OR r2=(r )2∗100=_____%

NEXT CLASS: TOPICS: Normal Distribution DUE: EC#5Stat Essentials (taken from today): Review from prior classes 1) Steps leading to correlation and regression; 2) building and interpreting: scatter plot; hypotheses; correlation, statistical sig. of r; Today: 3) Regression – developing the regression equation; 4) terminology related to correlation & regression.

Problem 18.1: Determine the regression line for the Woodpecker data (problem 17.1)

Problem 18.2: Given the following data set obtain: 1) in words identify what the null and alternative hypotheses state for this set of data; 2) a correlation coefficient; 3) the significance level of the correlation; 4) the coefficient of determination; 5) the regression equation for the line of best fit; 6) Add the regression line to the scatter plot to right (approximate location); and 7) calculate values for Yogi and Booboo.

Lengths & Weights of Male Bears Length (in.): 53.0 67.5 72.0 72.0 73.5 68.5 73.0 37.0Weight (lbs.): 80 344 416 348 262 360 332 34

In words state the null and alternative hypotheses for these two variables.

H0: ρ=0 ________________________________________________

Ha: ρ≠0 ________________________________________________

r = ____ Sig. level of r = _____ r2 = _____ %

Regression Equation for these variables: ______________________

Given the regression equation you identified estimate the weight of the following two bears:

Yogi who is 76.0 inches long. Booboo (aka Bobo) who is 43 inches long.

Estimated weights: Yogi: ________________________________________________

Booboo: ______________________________________________

1810.29.19

32

STAT 101

TOPICS: Normal Distribution; Standard Normal Table DOCUMENTS:

HANDOUTS: Green #19; Yellow #19; Standard Normal Table; Practice Sheets; CA#5 AVAILABLE ONLINE: Green #19; Yellow #19; Normal Distribution and

Distribution of Sample Means PowerPoints; Anatomy (2): Normal Distribution, Standard Normal; CA#5

ASSIGNMENT: Text Readings: – CH. 6 sections 6.1-6.2 Text Problems: – none Items below: Do 19.1 & 19.2 [do 19.3-19.6 if we get do the practice sheet] CA#5

FORMULAS: Probability Rules: 1) ΣP (X )=1 2) 0≤P(X )≤1 z= x−μσ

z= x−xs

NEXT CLASS: TOPIC: Normal Distribution, Dist. Of Sample Means; DUE CA#5; Quiz #4 (corr. & reg., std. normal)Statistics Essentials: Know: 1) the characteristics of a standard normal distribution; 2) how to identify a probability distribution; 3) find an area associated with a z-score (use the standard normal table); 4) find a z-score associated with an area (use the standard normal table

Problem 19.1: Identify the area associated Problem 19.2: Identify the z-score associatedwith the following z-scores. with the following areas.

1) z = -1.54: area = 2) z = .50: area = 1) area = .0207: z = 2) area = .5000: z =

3) z = 2.33: area = 4) z = -1.645: area = 3) area = .9500: z = 4) area = .9900: z =

Draw the area under the standard normal curve and determine the probability noted.Problem 19.3: P(z ¿ 1.62) Problem 19.4: P(-.42 ¿ z or z ¿ .42)

Problem 19.5: P(1.00 ¿ z ¿ 2.50) Problem 19.6: P(-.26 ¿ z ¿ 0.00)

1910.31.19

33

STAT 101

TOPICS: Non-Standard Normal DistributionsDOCUMENTS:

HANDOUTS:; Green #20; Yellow #20; Quiz #4 AVAILABLE ONLINE: Green #20; Yellow #20; Dist. Of Sample Means ppt.; Normal

Dist. Ppt.; Confidence Intervals Ppt.HWK:

Text Readings: Ch. 7, section 7.1 Text Problems: p. 385 #8-12, 15-16, 27-28, 48-51,75 Problems from Yellow #19 – ones we do not get to in class Items below

FORMULAS: Dist. Sample Means: μx=μ σ x=

σ√n

z= x−μσ√n ; Pop:

μ=∑i=1

n

x i

N σ=√∑ x2

N−μ2

NEXT CLASS: TOPICS: Dist. Of Sample Means (cont.?); Confidence Intervals (?) DUE: noneStatistics Essentials: Know: 1) application of standard normal to non-standard normal situations; and, if we get there: 2) the characteristics of the distribution of sample means; 3) the Central Limit Theorem.

Problem 20.1: Driven to distraction: It seems almost silly to say: Keep your eyes on the road. But with cars now more than ever resembling mobile offices, massive entertainment centers, telephone booths and lunch counters – well, the road is sometimes the last thing we’re looking at. It’s much more interesting to jabber away on the cell phone or toy with your iPod – but those distractions can cut your reaction time in half. And with most accidents occurring within a few seconds, you need all the time you can get. So hang up, find a radio station you like and keep looking forward. (Source: MetLife yourlife, Summer 2007; italics added)

So what do you know? Assume it takes you 2 seconds to react and apply the brakes when driving and paying attention to the road. How long will it take you to react while being distracted by food, phone, etc?

Problem 20.2: Marriage Patterns: Are more people living together before getting married? The results of a recent survey indicated that 48% of respondents indicated that they were in an unwed relationship and that forty percent of these couples marry within three years. If there were 1200 respondents to the survey, how many of the respondents would marry within three years?

Problem 20.3: Education and self-employment: According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean if 13.6 and a standard deviation of 3.0.

If one self-employed person was randomly selected, what would be the probability that he/she would have an education level less than 11 years?

Problem 20.4: Pregnancy Duration: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

Wanda has been pregnant for a really, really long time. So long in fact that only one-half of a percent of women have been pregnant longer. For how many days has Wanda been pregnant?

2011.5.19

34

STAT 101

TOPICS: Non-Standard Normal Dist.; Dist. of Sample Means; Central Limit TheoremDOCUMENTS:

HANDOUTS: Green #21 AVAILABLE ONLINE: Green #21; Dist. Of Sample Means ppt.; Confidence Intervals

Ppt.HWK:

Text Readings: Ch. 7, section 7.1 Text Problems: none CA#6 Problems from Yellow #19 & 20 – try some problems we did not get to in class; KEYS are online Items below

FORMULAS: Dist. Sample Means: μx=μ σ x=

σ√n

z= x−μσ√n ; Pop:

μ=∑i=1

n

xi

N σ=√∑ x2

N−μ2

NEXT CLASS: Confidence Intervals DUE: CA#6Statistics Essentials: Know: 1) application of standard normal to non-standard normal situations; 2) the characteristics of the distribution of sample means; 3) the Central Limit Theorem; 4) application to non-standard normal where n > 1.

Problem 21.1 (NOTE: continuation of 20.3)Education and self-employment: According to a recent Current Population Reports, the population distribution of number of years of education for self-employed individuals in the United States has a mean if 13.6 and a standard deviation of 3.0.

Find the mean and standard error of the sampling distribution of the mean for a random sample of size 100.

If a sample of 100 self-employed individuals is selected, find the probability that their mean education level is less than 11.0 years.

Problem 21.2: Normal Distribution: PINE TREES: A buyer for the You-Build-It Lumber Company must decide whether or not to buy logging rights on a piece of land containing 15,000 mature pine trees. The heights of mature pine trees are normally distributed and the owner reports that the trees have a mean height of 36 feet and a standard deviation of 4 feet. The buyer will purchase the logging rights if less than 1,000 of the trees are estimated to be shorter than 30 feet tall. Based upon this information, what is the buyer’s decision?

A) Draw a picture of this problem.

B) How many trees are estimated to be shorter than 30 feet tall? ______

C) Explain your answer (i.e. show how you came to your recommendation).

D) According to the stipulations cited above, is this a BUY ______ or a DO NOT BUY _______ situation?

2111.7.19

35

Problem 21.3Box plot: The table to the right contains the amount of fat per serving in grams of 12 Kelloggs “Children’s” cereals. Construct a box plot of these data.

Min: _____ Q1: _____ Q2: _____ Q3: _____ Max: _____ IQR: _____ L. Limit: _____ U. Limit: _____

Place Box Plot Here:

Problem 21.4Correlation & Regression:

Standard error of mean versus standard deviation. ... Put simply, the standard error of the sample mean is an estimate of how far the sample mean is likely to be from the population

These data were obtained from a survey of the number of years people smoked

and the percentage of lung damage they sustained.Years, x Damage, y x2 y2 xy

22 20 484 400 44014 14 196 196 19631 54 961 2916 167436 63 1296 3969 22689 17 81 289 153

41 71 1681 5041 291119 23 361 529 437

Sum 172 262 5060 13340 8079

a) Calculate the correlation coefficient and determine if the variables have a sig. corr.b) Find the equation of the regression line.c) Construct a scatter plot of the data.d) Predict the percentage of lung damage for a person who has smoked for 30 years.

36

mean, whereas the standard deviation of the sample is the degree to which individuals within the sample differ from the sample mean.

37

STAT 101

TOPICS: Confidence Intervals DOCUMENTS:

HANDOUTS: Green #22; Yellow #22 AVAILABLE ONLINE: Green #22; Yellow #22; Anatomy Sheets for Confidence Intervals;

Confidence Intervals ppt RELEVANT ANATOMY SHEETS (4): Z, Confidence Intervals for Small Samples, Large Samples, &

ProportionsASSIGNMENTS:

Text Readings: – Ch. 8, sections 8.1 – 8.3 EX#6 Item(s) below.

FORMULAS: Confidence Intervals & sample sizes [NOTE: Probabilities are on Orange #19]

x±zα2( σ√n ) x±zα

2( s√n ) x±t α

2, df ( s√n )

p¿±zα

2¿¿

n=( zα2σ

E )2

n= p̂ q̂( zα

2

E )2

NEXT CLASS: TOPIC: Confidence Intervals; DUE: EX#6Statistics Essentials for Confidence Intervals: Know: 1) what a confidence interval represents and how to calculate one for specific conditions; 2) what a margin of error is and how to obtain it; 3) the table above; 4) obtaining Z critical values.

Problem 22.1 Pregnancy Duration: The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

Find the mean and standard error of the sampling distribution of the mean for a random sample 10 pregnancies.

A sample of 10 pregnant women is selected. Find the probability that their mean pregnancy is greater than 283 days.

Problem 22.2 Critical Value of za/2: Calculate the za/2 critical value associated with the following Confidence Levels.

92%: za/2 = _______ 96%: za/2 = ______ 90%: za/2 = _______ 98%: za/2 = _______

2211.12.19

C onfidence Intervals for a Mean C onfidence Intervals for a P roportion

X % C .I. = X % C .I. =

S ample S ize

sknown:

s known:sunknown)

30

n

x z s

2

30

nx z s

2

nsx t df,2

nsx z 2

)(__

ExEx

npqp z 2

)( EpEp

38

Problem 22.3Balance-1: Data were collected on the length of time subjects could stand on one foot with eyes closed? Using the data provided in the accompanying table for a random sample of 30 time measures (from N = 94), build 95% confidence intervals about the observed means for left foot up and right foot up.

Problem 22.4Balance-2: Using the data from the prior problem, obtain a 90% confidence interval for the left foot up data.

Problem 22.5Balance-3: Examine the Left Foot 90% and 95% confidence intervals from the prior problems. What happened to confidence and precision when going from a 90% C.I. to a 95% C.I? Explain why this happens?

Problem 22.6Balance-4: The N = 94 statistics table to the right presents the mean, , and standard deviation, s, for the studied population. Review the means and determine if they fall within the 95% confidence intervals generated in the previous problems for the samples of size n = 30. Can samples be used to estimate population parameters? What would be some advantages of using samples to estimate population parameters?

39

STAT 101

TOPICS: Confidence Intervals for Small Samples & Proportions; C.I. sample sizesDOCUMENTS:

HANDOUTS: Green #23; Yellow #23 AVAILABLE ONLINE: Green #23; Yellow #23; Hypothesis Testing ppt.

ASSIGNMENT: Text Readings: – Ch. 8, sections 8.1 – 8.3 Yellow #23: problems #5, 6, 14, 18 Items below and Green problems 22.3-22.6 EX#6

FORMULAS: On prior sheets (Confidence intervals on sheet #22).NEXT CLASS: TOPICS: Hypothesis Testing DUE: EX#6Statistics Essentials for Confidence Intervals (proportions): Know: 1) how to identify a confidence interval for small samples & proportions; 2) Calculating the intervals; 3) characteristics of the t distribution.

Problem 23.1 (Correlation)Trees: Heights and Diameters The height (in feet) and trunk diameters (in inches) of 11 trees are shown below.

Height, x Diameter, y x2 y2 xy70 8.3 4900 68.89 58172 10.5 5184 110.25 75675 11 5625 121 82576 11.4 5776 129.96 866.471 9.2 5041 84.64 653.273 10.9 5329 118.81 795.785 14.9 7225 222.01 1266.578 14 6084 196 109277 16.3 5929 265.69 1255.180 18 6400 324 144082 15.8 6724 249.64 1295.6

Sum 839 140.3 64217 1890.89 10826.5

a) Calculate the correlation coefficient and determine if the variables have a significant correlation. b) Find the equation of the regression line.c) Construct a scatter plot of the data.d) Using the regression equation, what is the predicted diameter for x=74 feet? 81 feet? 95 feet? 79 feet?

Problem 23.2 (Confidence Interval)Health Clubs: A random sample of 60 female members of health clubs in Los Angles showed that they spend on average 4 hours per week doing physical exercise with a standard deviation of .75 hours. Find a 95% confidence interval for the population mean

Problem 23.3: (Normal Distribution)Tall Clubs International: Tall Clubs International is a social organization for tall people. It has a requirement that men must be at least 74 inches tall, and women must be at least 70 inches tall. Man’s heights are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches. Women’s heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches.

A) What percent of men meet the requirement?B) What percent of women meet the requirement?

C) Are the height requirements for men and women fair? Why or why not?

2311.14.19

40

TAT 101

TOPICS: Hypothesis Testing (One Sample)DOCUMENTS:

HANDOUTS: Green #24; Yellow #24 AVAILABLE ONLINE: Green #24; Yellow #24; EX#7; Hypothesis Testing ppt; REVIEW

SHEETS #1-5ASSIGNMENT:

Text: Ch. 9, section 9.1 – 9.4 Text Problems: none EX#7 & EX#9 (emailed at 5 PM) Items below

FORMULAS: Hypothesis Testing

z=x−μ0

σ√n

t=x−μ0

s√n

z= p¿̂−p

√ pqn

¿

Steps in testing a hypothesis:1. List the given information2. State in statistical and word format the null hypothesis and the alternative hypothesis

a. Identify the “claim”3. Determine if the test is one-tailed (left or right) or two-tailed4. Identify the critical value for the test (or the stated p-value level at which the test is being conducted)5. Draw a picture containing the critical value(s) and, after testing, the test statistic6. Identify the statistical test7. Conduct the test and obtain the test statistic (place it on your drawing)8. Analyze your results (relationship between critical value and test statistic (or p-values comparison)9. State a conclusion. Include a statement of the null hypothesis, the level at which it was tested, and whether it was retained

or rejected.NEXT CLASS: TOPICS: Hypothesis Testing; DUE: EX#7Statistics Essentials Hypothesis Testing: Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p-value, etc.; 4) how to conduct a hypothesis test and interpret the results.

Problem 24.1: (Hypothesis)Doctor Salaries: Is there a doctor in the house? The Bureau of Labor Statistics reported that in May 2009, the mean annual earnings of all family practitioners in the United States was $168,550. A random sample of 55 family practitioners in Missouri that month had mean earnings of $154,590 with a standard deviation of $42,750. Do the data provide sufficient evidence at to conclude that the mean salary for family practitioners in Missouri is less than the national average?

Problem 24.2: (C.I. Proportions)New Year’s Resolution: From a recent survey of 2241 U.S. adults, 29 % of respondents indicated that they had made a resolution to eat healthier. (L&F 7ed p.325, #12 & 21)

a) Determine the number of individuals indicating an intent to eat healthier.

b) Construct a 90% confidence interval for the population proportion.

24

Testing a Hypothesis

Decision: TRUE FALSERETAIN

Correct Type II ErrorDecision b

REJECT Type I Error Correct Decision

Null Hypothesis

41

Problem 24.3: (C.I. Small Sample)Commute Time: From a random sample of eight people, the mean commute time to work was 35.5 minutes with a standard deviation of 5.8 minutes. Build a 95% confidence interval about the sample mean, for the population mean. (L&F 7ed p.315, #17)

Problem 24.4: (Normal Distribution)Test Scores: Assume the test scores for a large class are normally distributed with a mean of 74 and a standard deviation of 10. (Le p.144, #3.14)

a) Suppose that you received a score of 88. What portion of the class received scores higher than you?

b) Suppose that the instructor wants to limit the number of A grades to 20%. What would be the lowest score for an A?

42

STAT 101

TOPICS: Hypothesis Testing (One Sample)DOCUMENTS:

HANDOUTS: Green #25 AVAILABLE ONLINE: Green #25; Hypothesis Testing ppt; STAT EXAM #2 REVIEW

SHEETS #1-5ASSIGNMENT:

Text: Ch. 9 sections 9.1-9.4 Text: none CA#7 NOTE: THIS WILL NOT BE ACCEPTED FOR

ANY REASON (INCLUDING LEGAL EXCUSES) AFTER TUESDAY NOVEMBER 26. BEYOND THAT DATE IT BECOMES AN “N” GRADE.

Items below FORMULAS: Hypothesis Testing

z=x−μ0

σ√n

t=x−μ0

s√n

z= p¿̂−p

√ pqn

¿

Steps in testing a hypothesis:1. List the given information2. State in statistical and word format the null hypothesis and the alternative hypothesis

a. Identify the “claim”3. Determine if the test is one-tailed (left or right) or two-tailed4. Identify the critical value for the test (or the stated p-value level at which the test is being conducted)5. Draw a picture containing the critical value(s) and, after testing, the test statistic6. Identify the statistical test7. Conduct the test and obtain the test statistic (place it on your drawing)8. Analyze your results (relationship between critical value and test statistic (or p-values comparison)9. State a conclusion. Include a statement of the null hypothesis, the level at which it was tested, and whether it was retained

or rejected.NEXT CLASS: TOPICS: Hypothesis Testing/ Exam #2 Review DUE: CA#7Statistics Essentials Hypothesis Testing: Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p-value, etc.; 4) how to conduct a hypothesis test and interpret the results.

Problem 25.1:

Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO credit score is lower than the cutoff of 720. She finds that a random sample of 100 people had a mean FICO score of 703 with a standard deviation of 92. Can the economist conclude that the mean FICO score is less than 720? Use α=.05 level of significance.

Problem 25.2: Measuring lung function: One of the measurements used to determine the health of a person’s lungs is the amount of air a person can exhale under force in one second. This is called the forced expiratory volume in one second, and is abbreviated FEV1. Assume the mean FEV1 for 10-year-old boys is 2.1 liters and that the standard deviation is 0.3. A random sample of 100 10-year-old boys who live in a community with high levels of ozone pollution are found to have a sample mean FEV1 of 1.95 liters. Can you conclude that the mean FEV1 in the high-pollution community is less than 2.1 liters? Use the α = 0.05 level of significance.

Problem 25.3: Environment: In 2008, the General Social Survey asked 1493 U.S. adults to rate their level of interest in environmental issues. Of these, 751 said that they were “very interested.” Does the survey provide convincing evidence that more than half of U.S. adults are very interested in environmental issues? Use the α=.05 level of significance.

25

Testing a Hypothesis

Decision: TRUE FALSERETAIN

Correct Type II ErrorDecision b

REJECT Type I Error Correct Decision

Null Hypothesis

43

Testing a hypothesis: (format to be used for upcoming exam)

1) Provide a complete list of the GIVEN information:

2) State the null and alternative hypotheses in both statistical form and written form AND identify the Claim being made by checking one of the two boxes located at end of the written description.

Statistically: In Words: Claim(check one)

Ho: ________________ Ho: _________________________________________________________

Ha: _________________ Ha: _________________________________________________________

3) The hypothesis test is (circle one): one-tailed, tailed one-tailed, right two-tailed

4) Identify the Critical Value(s) for the test. C.V. = __________

5) Draw a detailed picture displaying the region(s) of retention and rejection of the null hypothesis. Include the location of the Critical Value(s) and Test Statistic (once calculated).

Present the formula to be used, determine the Test Statistic and locate the T.S. on the picture.

Show Formula, Calculations and test statistic

6) State Formula:

Calculations:

7) Test Statistic: _____________ (place here and on diagram)

8) Analyze: The results indicate that we should (circle one): REJECT H0 RETAIN H0 Beyond that decision, just review results so you can address step 9).

9) Using the general format presented in class, state a conclusion for this hypothesis test.

________________________________________________________________________________________________

________________________________________________________________________________________________

________________________________________________________________________________________________

________________________________________________________________________________________________

step 5) EE

44

________________________________________________________________________________________________STAT 101

TOPICS: Hypothesis Testing for Proportions DOCUMENTS:

HANDOUTS: Green #26; Exam #2 Take-home Problem AVAILABLE ONLINE: Green #26; NOTE: Part 1 of Exam #2 will be placed online

in the “CLASS ASSIGNMENTS” section for students absent from class on Nov.26. HWK:

EXAM #2 TAKE-HOME PROBLEMFORMULAS: Available on prior green handouts THE FINAL THREE DAYS:

12/3 – Exam #2 12/5 – data collection for Lab #2 12/12 & 12/17 – Application Lab

NEXT CLASS: TOPIC: EXAM #2 DUE AT CLASS TIME: Exam #2 Take-home portionStatistics Essentials: Know: 1) how to write hypotheses in statistical format and in written format; 2) what statistical significance means; 3) what terms associated with hypothesis testing mean – e.g. critical value(s), test statistic, p value, etc.; 4) how to conduct a hypothesis test and interpret the results.

EXAM #2 Review Topics: Descriptive Statistics: Obtaining Statistics – Measures of Center & Variation. Measures of Position – five-number summary, modified box plots with associated calculations; skewness; z-score;

CVAR; etc. Correlation & Regression – scatter plots, r, r2, least squares line, calculating regression estimates Normal distribution – standard normal table, finding areas or z values; non-standard normal data, finding

probabilities and variable values

Distribution of sample means - μx ,σ x , central limit theorem, problems where n>1 Confidence Intervals - s vs. s, < 30 vs.≥ 30, intervals for proportions, finding x and E given interval, Standard

Normal table, t-table, determining sample size for means problems Hypothesis Testing – one sample for means and proportions

REFERENCES/STUDY MATERIALSo Green Sheet - Keys onlineo Yellow Sheet - Keys online (most)o Course Review Materials – Additional problems & KEYS for areas since Exam #2 (online Supporting

Materials link)o Text problemso Topic-based PowerPointso Anatomy of Statistics Sheetso Essential Statistics: the first PowerPoint – listing items to knowo Statistics Essentials: Review this section of each Green sheet. Can you do these things? o In-class review sheet (Tuesday Nov. 26). Available online as Exam #2 Review Sheet #6.o Office Hours: T & Th: 8-8:20; 11:20-12; 1:30-2:20; 4:00 – 5:00o Must be something else…

2611.26.19

45

Problem 26.1: Curing diabetes: vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with type 2 diabetes underwent this procedure, and 59 of them experienced a recovery from diabetes. Does this study provide convincing evidence that more than 60% of those with diabetes who undergo this surgery will recover from diabetes? Use the α=.05 level of significance.

Problem 26.2:High salaries for executives: A Washington Post-ABC News poll conducted in October 2009 surveyed a random sample of 1004 adults in the United States. Of these people, 713 said they would support federal legislation putting limits on the amounts that top executives are paid at companies that receive emergency government loans. One highly paid executive claims that less than 75% of U.S. adults support limits on the amounts that executives are paid.

a) State the appropriate null and alternate hypotheses.b) Compute the test statistic.c) Using α=.05, can you conclude that the executive’s claim is true?d) Using α=.01, can you conclude that the executive’s claim is true?

46

STAT 101 NAME: _________________________________

TOPICS: Data Collection [6 points]; Exam Review DOCUMENTS:

HANDOUTS: Green #27 AVAILABLE ONLINE: Green #27

HWK: REVIEW FINAL EXAM DATE AND LOCATION LISTED ON GREEN 27

NEXT CLASS: TOPIC: Lab Data Analysis

1) Place your data on this sheet2) Enter your data into the computer file.3) Answer the questions below.4) Leave this form in the three-ringed binder.

Data Collection & Entry [3]:BENTON'S INDIVIDUAL COOKIE WEIGHTS (grams) OREO INDIVIDUAL COOKIE FILLING WEIGHT (gms)

COOKIE Benton's Plain Wt.

FILLING Benton's Plain Wt.

COOKIE Benton's

Double Wt.

FILLING Benton's

Double Wt.COOKIE Oreo

Plain Wt.FILLING Oreo

Plain Wt.COOKIE Oreo

Double Wt.FILLING Oreo

Double Wt.

Cookie Stats:

Questions: For each of the following items think of the various descriptive and inferential statistics we have explored, generate a question that could be explored during the final class meeting, and what we might learn via that investigation.

Example: Normal Distribution: What - Examine the weights of double-stuf cookies (whole or filling) to determine proportion of cookies within a pre-determined weight range. Why – an opportunity determine the consistency of cookie production with regard to weight component.

1) Descriptive tables, graphs & statistics [1]:

What: ________________________________________________________________________________________

Why: _________________________________________________________________________________________

2) Confidence Intervals [1]:

What: ________________________________________________________________________________________

Why: _________________________________________________________________________________________

3) Hypothesis Testing [1]:

What: ________________________________________________________________________________________

Why: _________________________________________________________________________________________

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STAT 101

TOPICS: Exam #2 DOCUMENTS:

HANDOUTS: Green #28 AVAILABLE ONLINE: Green #28

HWK: None

NEXT CLASS: TOPICS: data collection for the final’s week lab.

UPCOMING CLASS SCHEDULE

FINALS WEEK:

8:30 AM CLASS:THURSDAY DEC. 12, 2019LOCATION: Milne Library 305 (computer lab)CLASS EXAM TIME: 8:00 – 10:30

10:00 AM CLASS: TUESDAY DEC. 17, 2019LOCATION: SCHUMACHER 09 (in basement)CLASS EXAM TIME: 8:00 – 10:30

2:30 PM CLASS: THURSDAY DEC. 12, 2019LOCATION: Milne Library 305 (computer lab)CLASS EXAM TIME: 2:00 – 4:30

Finals Class Schedule of Events, etc: Course Evaluation followed by Data analysis completed individually or in groups of 2-3 max. Resources: Bring any books, handouts, notes, consultants, etc. that you feel may be of help in the data analysis. IF YOU ARRIVE LATE, YOU MUST COMPLETE THE LAB PROJECT ON YOUR

OWN.Ah, Statistics…

The government are very keen on amassing statistics. They collect them, add them, raise them to the nth power, take the cube root and prepare wonderful diagrams. But you must never forget that every one of these figures comes in the first instance from the village watchman, who just puts down what he damn pleases. [--Comment of an English judge on the subject of Indian statistics; Quoted by Sir Josiah Stamp in _Some Economic Matters in Modern Life_]

There are three types of people in this world: Those who can count, and those who can't. [Seen on a bumper sticker]

The statistics on sanity are that one out of every four Americans is suffering from some form of mental illness. Think of your three best friends. If they're okay, then it's you. [Rita Mae Brown]

I always find that statistics are hard to swallow and impossible to digest. The only one I can remember is that if all the people who go to sleep in church were laid end to end they would be a lot more comfortable. [Mrs. Robert A. Taft]

Before the curse of statistics fell upon mankind we lived a happy, innocent life, full of merriment and go, and informed by fairly good judgment. [Hilarie Belloc The Silence of the Sea]

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NOTE: College policy holds that the final exam (for us #2) must be retained by the faculty member. To assure that this policy is followed, you may not receive credit (up to 30 points) for participation in the final class lab session without exam two’s return.

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