Download pdf - AP Stat Packet

7/31/2019 AP Stat Packet

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Preston H. Earle

AP Statics Summer Work

Preliminary Exercises

P.1. Jamies preference is not good evidence that most young people prefer Jolt to Coke or

Pepsi because Jamie and her friends do not accurately represent the whole of the population. This

population could very easily lead to bias because the sample taken is of a small and very specific

group of people. The sample should be random.

P.2. a. The study of a direct correlation between the use cell phones and brain cancer is

observational because the conclusion is drawn using pre-existing data rather than actually

conducting an experiment.

b. No, the conclusion that there is a direct correlation between cell phone usage and brain

cancer would be imprudent. Irrefutable scientific conclusions must be made from precise, welldeveloped experiments.

P.3. a. The study of the effectiveness of an educational software companys computer

animation program for biology as opposed to a textbook presentation is an experiment. This is an

experiment because the software company actually conducted tests on two random groups of

high school juniors and then drew conclusions.

b. If the group of high school juniors using the computer program achieved a much

higher average than that of the juniors using the textbook, then the conclusion could be made that

the computer animation software is more effective than the traditional textbook.

P.4. a. If someone was to find out if people were generally satisfied with how things are going

in the country right now, then a survey would need to be conducted. The reason a survey would

need to be carried out rather than an experiment or observational study is that this is a simple

question being posed to the population. There are no variables to test or behaviors or correlations

to analyze.

b. If someone to test whether college students learn accounting better in a classroom or

using an online course, then an experiment would need to be conducted. The reason an

experiment would need to be conducted rather than a survey or observational study is that this

must be tested. There are variables to test and data to analyze in order to draw a conclusion. No

simple question can be asked nor can this be analyzed because students could easily show bias

towards one option or the other.

c. If someone wanted to determine how long teachers wait on average after they ask their

classes a question, then an observational study would be the most logical decision. This fact can


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easily be discovered by observing teachers. A question cannot be asked and an experiment is not

necessary because it is a simple observation, not a test or comparison.

P.5. a. In an observational study of the health of people who drink wine as opposed to people

who drink beer, some rather unorthodox methods would have to be used. Observing in this

case would be viewing health records, physicals, or some other medical examination that wouldidentify the good or bad health of the random strangers found at a bar or other location which

provides alcohol. In an observational study, there is now empirical data to show how often the

person drinks or if that person exclusively drinks one type of alcohol. An experiment, the more

rational choice, would entail selecting a group people who are carefully monitored and analyzed

in a controlled environment. These people would be split into two equal but separate groups, and

their health would be tested before, during, and after the experiment. This controlled

environment would allow for precise conclusion; whereas, the observational study would have

too many variables which could not be controlled.

b. One could infer that people who drink wine are slightly wealthier than people whodrink beer by virtue of the fact that wine is generally more expensive. People who can afford the

finer things like wine could also afford good health insurance and good doctors. They could

also afford healthier, organic food which would lead to better health.

P.6. According to the National Center for Education Statistics, 76 percent of all full-time

dependent students worked while enrolled in college in the year 2000. However, a study

conducted by Upromise Incorporated under the direction of Jonathan M. Orszag, Peter R.

Orszag, and Diane M. Whitmore concluded that the numbers were significantly lower. In the

graph below, the conclusion was drawn that the college employment rate never reached above 60

percent.


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P.7. a.

b. It is obvious that the colors which are the most subtle and ordinary are also the most

popular. Silver and White, two very common, ordinary colors, were by far the most popular. Onecan see that the more vibrant and further away from the grayscale the car is, the less popular it

becomes. It is also interesting to note that this small amount of colors take over 85 percent of the

entire 2003 model year. All other colors combined only add up to 14.2 percent.


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P.8. a.

b. It is clear that the data from P.7 correlates to the data in P.8. Silver and White are again

the most popular for both Luxury and SUV cars. It also seems that the more subtle colors, Silver,White, Black, and Gray are more popular in Luxury cars; whereas, the slightly more vibrant

Blue, Green, and Red are more popular in the SUV/Truck/Van category.

P.9. a.

Dot Plot of U.S Womens Soccer Scores (Differential)

b. This dot plot shows that only a few games were lost, and only a few games were tied.

Most of the games were won and generally by small margins. There is a steady declining trend

which develops from 1 onto 8. Fewer games are one at high score differences.


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P.10. a.This dot plot shows the amount of gold medals earned by a set of 30 countries. Most ofthe countries did not win any gold medals, and most of the data lies between 0 and 9. One

extreme outlier, the United States, won 35 medals. Because of the great amount of 0s and large

range, the distribution of this graph is not even.

b. Yes, the sample is an accurate representation of the larger population by virtue of the

amount of teams who did not win any gold medals. An inaccurate representation would have

included mostly teams who won gold medals.

P.11. Class Survey

Who- The students in the AP Statistics Class What- Variables

o Categorical Variables- gender, hand, genre of musico Quantitative Variables- Height (inches), Homework Time

(minutes), coins (individual coins, currency and type of coin

are not specified)

Why- The teacher most likely wants to gather anonymous informationabout his students

When- On the first day of class Where- The data is collected from the teachers AP Statistics students

and is gathered anonymously

How- The data was gathered through an anonymous survey of thewhole AP Statistics class

By Whom- The surveyor is the teacher of the classP.12. Medical Study Variables

Categorical Quantitative

Gender Age

Race Systolic Blood Pressure

Smoker/Non-smoker Calcium Level in Blood


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P.13. Two categorical variables which could be used in a TV viewing habits study would

include gender and the genre of television being watched; two quantitative variables could be

time spent watching television each day and how many days a week the person watches

television.

P.14. The probability of rolling a 6 on a six-sided die is 1/6. This is the case because it is one

number being rolled for out of 6 possible outcomes. Theoretical ly, the die should on the 6 one

out of every six times; however, this does not manifest itself after only 6 rolls. In order for this

probability to be seen, the die must be rolled many times. The more the die is rolled, the more

accurate the probability will become.

P.15. 14 out 21 identifications would clearly be the better outcome. This would show that Mr.

Bullards class could more easily identify the type of water being tasted. As the the number of

students that can identify the water type increases, the likelihood that people can taste the

difference also increases.

P.16. I dont imagine the probability being any higher than 0.05. It is very unlikely that 11 or

more children guessed correctly. It is more likely that the students could distinguish the different

types of water.

P.17.

Coin Flipping

Toss Number Heads Tails

1 - +

2 + -

3 + -

4 - +

5 - +

6 + -

7 + -

8 - +

9 - +

10 - +

11 + -

12 - +

13 - +

14 + -

15 + -16 - +

17 + -

18 - +

19 + -

20 + -

Total- 20 10 10


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a.

b. The proportion ended in exactly half (0.5).

c. The conclusion can be made that the more times the coin is flipped, the closer the

proportion comes to 0.5. This seen through the data provided. The proportions deviation slowlydecreases until it reaches a precise .

P.18. a. No, if Gallup asked all teens aged 13 to 17, their number would be at least slightly

different because all samples have different variability.

b. Absolutely. The margin between boys and girls saying yes is 16%. No matter how

large the sample becomes, the girls will always have a higher percentage. Not only is this

statistically true, it is also biologically and anatomically sound. Boys also dont have to live with

the ramifications of their actions- pregnancy.

P.19. a. This is an observational study because the people did not experiment on the children.

They simply observed their reaction to the violence on the television.

b. If the child is neglected, he or she may result to occupying time with senseless violent

television; however, if a child were to act out violently, this could be a cry for attention due to

negligence, not necessarily related to the TV.


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P.20. According to the National Highway Traffic Safety Administration, 35 percent of teen

deaths (15- 20 years old) are caused by motor vehicle accidents. This is seen here, in the pie

chart on the NHTSA website under the Teen section.

Also found in the teen section of the NHTSA are four main topics presented as

thumbnails. When these four thumbnails are clicked on, four different statistical summaries of

teen-driving appear. These analyses are as follows:

Seat Belt Use

Youth Access to Alcohol

Graduated Driver Licensing

Parents and Teens

In Seat Belt Use, it is said that teens wear seat belts significantly less often than their

parents do. According a study in 2008, only 80 percent of teens (16-24 years old) use a seat belt.

This 80 percent is the lowest of any age group. This apathetic attitude towards seat belts is not

only laze, but also lethal. In fact, the NHTSA states the majority (56%) of young people 16 to

20 years old involved in fatal crashes were unbuckled.

In Youth Access to Alcohol, it is stated that despite it is illegal for teens to purchase

and consume alcohol, they are still at a much greater risk of death than adults due to

consumption of alcohol. Although no specific statistics are stated, it is clear that an emphasis has

been placed on protecting teens from the abuse of alcohol.

In Graduated Driver Licensing, a 3 stage system of driving is illustrated. This system is

used by 46 of the 50 states and the District of Columbia. This 3 stage system consists of a

learners permit, a provisional license, and then a full license at the age of 18. It has also beenshown that this 3 stage program brings fatality rates up to 50 percent. This information is found

in a link underReportsin an article called Graduated Driver Licensing System.


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In Parents and Teens, there is a strong emphasis on rules which all parents should

impose upon their children when driving. Three big guidelines are given. These guidelines are

Talk to your Child, Set a Standard, and Spell out the Rules. The rules found in guideline 3

are as follows:

Alcohol: Absolutely No Alcohol Seat belts: Always Buckle Up! Cell phone/texting: No talking or texting while driving Curfew: Have the Car in the Driveway by 10 p.m. Passengers: No more than one at all times Graduated Drivers License: Follow the state's GDL law Parental Responsibility: Set your house rules and consequences

P. 21. Fuel Economy Study

Who- The types of Cars What- Variables

o Categorical- Make& Model, Vehicle Type,Transmission Type

o Quantitative- Number of Cylinders(1 individualcylinder), City MPG (measured in miles), Highway

MPG (measured in miles)

Why- to determine the most fuel efficient cars based on eachcars transmission, number of cylinders, and MPG

When- The data was collected in 2004

Where- The data is collected from motor vehicles involved inthe study

How- This data was gathered through observations of the carsfuel economy, transmissions, and number of cylinders

By whom- The data was collected by the governments officialFuel Economy source
http://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenalcohol.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenseatbelt.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenphones.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teennighttime.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenpassengers.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teengdl.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenrules.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenrules.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teengdl.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenpassengers.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teennighttime.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenphones.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenseatbelt.dochttp://www.nhtsa.gov/DOT/NHTSA/Traffic%20Injury%20Control/Teen%20Driver/files/teenalcohol.doc


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P.22. a.

It is clear that the freshman have the lowest percentage; this shows that freshman have

the lowest chance of hurting themselves. The other three grades are all relatively close in

percentage and have a significantly higher risk than freshman of getting hurt.

b.

This side by side graph shows the fact that girls often wear helmets more than boys and

are at less of a risk for injury. Just as the graph before, freshman have significantly lower

numbers than their older peers.


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P.23. If the probability of getting three of a kind is 1/50 in a five card per hand game, then a

person playing poker will most likely have at least one hand with 3 cards of the same number

after fifty hands have been dealt.

P.24. a. Gallup decided to survey a random sample of American Adults because if the survey

had been comprised of only attendees of a Major League Baseball game, the results may havebeen biased. Fans of baseball could have a deep admiration of Bonds or his team; but by the

same token, fans of other Major League teams or players could have a negative bias against

Bonds.

b. Due to the 3 percent deviation in all samples, the results of people responding

probably not could become anywhere from 39 to 45 percent; accordingly, the people who

responded definitely not would vary from 30 to 36 percent.

c. Absolutely not. No opinion could give an accurate answer. Only factual statistics can

determine truth. Even juries are never entirely certain of court cases. Since none of the people ofthe survey know Bonds or the people who gave him the creams, there is no way to accurately

determine Bonds culpability.

P.25. The conclusion could be drawn that the magnets are affective on postpolio patients, but

not as affective once thought. If the means are closer together, that means there is a closer

margin for error. The magnets are still effective, but it seems there are less effective when the

difference in means goes down from 4.05 to 2.5.


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P.26. a. Dot plot for Active Magnets

It appears that many people saw little to no change in pain in the active magnets;

however, the majority of the people felt a 4-8 point drop in pain. The same amount of people felt

no pain equaled the amount of people who felt the same amount of pain.

b. Dot plot for Inactive Magnets

There were many more people in the inactive group who felt no change in their pain, and

no one felt like their pain had completely vanished (lack of 10s). The majority of the people felt

like their pain was the same or was only slightly lower. Those who felt like their pain had

dropped by 4 or 5 points were most likely feeling a placebo effect.

c. The mean change for pain in active magnets is 5.241. The mean change for inactive

magnets was a mere 1.095.

d. One could conclude that the active magnets do really help treat pain in polio patients

because most patients felt considerable pain reductions; whereas, inactive magnet patients felt

little to no change in pain.


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P.27. Dot plot of MPG for Car Models in 2004

The highest MPG rates were 26, 28, and 25 in that order. The rates of 21, 22, 29, 32, 35

had no cars; 20, 23, 31, and 33 only had one car. The majority of the data is very close together

from 24-28.

P.28. a. The data was gathered through an observational study. The people did not directly

influence the children, nor did they force certain any students to become learned in the fine arts.

b. No, one could not definitively conclude that listening to Mozart directly affectschildrens test scores. Other variables may show this to be a mere coincidence. It would be fair to

say that children who have better test scores are more educated and cultured. This well-educated,

cultured personality could cause children to be steeped in Classical music such as Mozart.

c. An accurate, scientific way of determining whether Mozart for Minors is truly

positively effective on childrens test scores would be consist of a random sample of children put

into two separate groups. One group would be subject to Mozart for Minors, but the second

group would not be. Shortly after the groups are exposed to their musical programs (or lack

thereof), they would be given two tests. These tests would be over verbal skills and mathematics.

The results of these tests would then be compared.