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MM 207

Statistics

Unit 1

Instructor Scranton

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Population and Samle

Identifying the population and sample is a skill you will have to be familiar with on the quiz. So... for practice, let's identify the

Population and the Sample in the following exercise:

A survey of 2,359 American Households found that 94% of the households own a computer. Identify the population and the

sample.

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Solution/Explanation

The population is all American households. The sample is the 2,359 households that were surveyed for the study.

**The 94% is a sample statistic. It's interpretation is - 94% of the 2,359 households surveyed own a computer. You do not have to use the 94% to

answer any part of the question. However, since we took a sample, the 94% is a statistic (rather than a parameter).

I will take this opportunity to expand on the difference between population and sample. Please review this information carefully.

The population is the entire set/group that you would like to obtain information on. However this is not always possible. For example, I would like to know the

political opinions of all the adults in Missouri. It is not possible from a time, management, or monetary standpoint to obtain data from every person in Missouri. So I take a "sample" of the "population." The population is all the adults in the state of Missouri and the sample is the subset of adults that I

obtained the information from. Then I try to generalize my sample results back to the population.

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Parameter & Statistic Practice

1. A survey of 2625 elementary school children found that 28% of the children could be classified as obese. Identify the population and the sample. Identify any parameters or statistics.

2. The average salary of all General Motors workers is $42,000. Does this describe a population parameter or a sample statistic? Explain your reasoning.

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Solution/Explanation

#1. The population in this example equates to all elementary school children. It has a sample of 2,625 elementary school children. The statistic of the sample is that 28% of them are obese.

#2. The GM workers in this example represent a population parameter. It states "all GM workers" and states a characteristic about them without dividing them in in any manner/subgroup.

Class, since #2 is a population (all GM workers), the number 28% relates to the population. Therefore it is a parameter.

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Sample Size

Class, what do you think? Is 2,359 a large enough sample to represent all American households?

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Notes on Sample Size

Class, the following article provides the best explanation of this (sample size) that I have seen. Please read and report on what you find.

  http://www.publicagenda.org/pages/best-

estimates-guide-sample-size-and-margin-error   ...you may be surprised.

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20 questions you should ask…

Class, below I have posted an excellent article. This is a good one - it lists 20 questions that journalists should ask about poll results. Asking yourself these questions would help you determine whether you think a poll is accurate.

http://www.publicagenda.org/pages/20-questions-journalists-should-ask-about-poll-results

Which of these 20 questions do YOU think is most important? Anyone?

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Regarding Bias…

Here is a study about the flu in children. Please review it. Do you see evidence of possible bias? Where? Please comment.

http://www.usatoday.com/news/health/2006-07-05-flu-children_x.htm

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Sampling Techniques

For the following four questions determine which sampling technique was used from the list below.

Stratified cluster convenience systematic random

1. Thirty-five sophomores, 69 juniors and 24 seniors are randomly selected from 461 sophomores, 328 juniors and 558 seniors at a certain high school. What sampling technique is used.

2. Every fifth teenager entering a concert is checked for possession of drugs.

3. At a local community college, five statistics classes are randomly selected and all of the students from each class are interviewed.

4. A community college student interviews everyone in a statistics class to determine who owns a car.

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Solutions

1)Stratified2)Systematic3)Cluster4)Convenience

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Descriptive vs Inferential

1. The chances of winning the California Lottery are one chance in twenty-two million. Does this statement describe descriptive statistics or inferential statistics?

2. There is a relationship between smoking cigarettes and getting emphysema. Does this statement describe describe or inferential statistics?

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Solutions

The answer to both questions is "inferential." To summarize, I would classify both as inferential because they DO NOT involve the organization, summarization and display of data. Also, the first one is based on "probabilistic data" and the second is drawing an inference about a population ("There is a relationship"). In inferential statistics, probability is used as a basic tool."

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Level of measurement Practice

1. Identify the level of measurement for data that are the numbers of the shirts of a girl's soccer team.2. Identify the level of measurement for data that are the temperature of 60 refrigerators.3. Identify the level of measurement for data that are the number of milligrams of tar in 37 cigarettes.

 

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Solutions

1. Numbers of the shirts of a girl's soccer team.

Answer: Nominal level of measurement.

Data is categorized by labels, or qualities. No mathematical computations can be made with the numbers of the shirts.

2. The temperature of 60 refrigerators.

Answer: Interval level of measurement.

You can order the temperatures and calculate meaningful differences between the temps but not one value is a multiple of another.

3. Number of tar in 37 cigarettes.

Answer: Ratio level of measurement.

One data value can be meaningfully expressed as a multiple of another. You could add the milligrams from one cigarette to another to find the value in 37 cigarettes. You could also subtract a number of cigarettes from the total to find another amount.

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Qualitative vs Quantiative

1. Classify the colors of automobiles on a used car lot as qualitative or quantitative.

2. Classify the numbers on the shirts of a girl's soccer team as qualitative or quantitative.

3. Classify the number of seats in a movie theater as qualitative or quantitative.

 

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Solutions

1. Qualitative ==> Does not mention the number of each cars that are each color. Only the colors (e.g. red, blue, silver, black...)

2. Qualitative ==> because they are just labels.

3. Quantitative  

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WHERE IS STATCRUNCH

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Similar to an Excel Spreadsheet

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Enter Numbers

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Calculate Measures of Central Tendency and Variation

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