Submit (pdf) to Blackboard before midnight on Thursday, January 28, 2016.

1. Have you ever noticed that when a new restaurant opens around here, they are really crowded when they first open? Then, after some time, things calm down (and then I start thinking about going there. I still haven't been to Chili's in Russellville. Well, I did make it to the parking lot once when they had been open about 3 weeks. Then I saw the line of people waiting to go in and went somewhere else.). The Waiting.csv file includes data for the length of waiting time (time from when put name on list until time seated in restaurant) and the length of time the restaurant has been opened (first month, second month, third month).

a. Create a tabular summary that reports the sample size, mean, median, standard deviation, and interquartile range for each of the three months. Use statistical software to obtain the statistics. Use the guidelines for presenting tables posted in the FAQ tab on Blackboard.

b. Create a comparative boxplot for the data. Use statistical software to obtain the graph.

c. Create a comparative density plot for the data. Use statistical software to obtain the graph.

d. Interpret the numerical and visual summaries from parts a - c. (What are the key features of the data? How are the wait times distributed during each time period? Compare and contrast the wait times for the first three months.

2. Fill in the rest of the following table. (Nothing goes into the shaded cells.)

Score f rf Score cf crf
< 50
> 50 but < 60 6 < 60
> 60 but < 70 11 < 70
> 70 but < 80 17 <80
> 80 but < 90 9 < 90

> 90 but < 100 7 <100

3. A market research firm wants to determine if there is a difference in the amount of television viewed by people who introverted and people who are extroverted. Using the questionnaire and guidelines at http://www.jamescmccroskey.com/measures/introversion.htm, 50 introverts and 50 extroverts were identified. Each individual then answered the question "How many hours of television have you watched in the past 48 hours?" To increase participation rates, each person who completes the survey will be given $50. Data were collected between January 17 and January 19, 2016

a. Is this an observational study and not an experiment? Explain.

b. Explain the concept of confounding in the context of this study. Include an example of a possible confounding variable.

c. If the mean number of hours spent watching television was statistically significantly smaller for introverts (than for extroverts), should one conclude that the lower number of hours watching television can be attributed to level of introversion? Explain.

4. Consider the following data:
x
Y
6
5
12
9
8 7
6
8
4
15

a. Compute the sample means for x and y. Show all work, including symbols and formulas.

b. Compute the sample standard deviations for x and y. Show all work, including symbols and formulas.

c. Compute the covariance between x and y. Show all work, including symbols and formulas.

d. Compute the correlation between x and y. Show all work, including symbols and formulas.

NOTE: For multiple choice items, you can either handwrite the solutions and use a scanner or change the correct answer to boldface dark red.

5. You want to know the opinions of American school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers' union) and mail a questionnaire to 2500 teachers chosen at random from this list. In all 1,347 teachers return the questionnaire.
The sample is

a. the 1,347 teachers who mail back the questionnaire.
b. the 2,500 teachers to whom you mailed the questionnaire.
c. all members of the National Education Association.
d. all American school teachers.

e. all American school students.

6. An auto analyst is conducting a satisfaction survey, sampling from a list of 10,000 new car buyers. The list includes 2,500 Ford buyers, 2,500 GM buyers, 2,500 Honda buyers, and 2,500 Toyota buyers. The analyst selects a sample of 400 car buyers, by randomly sampling 100 buyers of each brand.
Is this an example of a simple random sample?
a. Yes, because each buyer in the sample was randomly sampled.
b. Yes, because each buyer in the sample had an equal chance of being sampled.
c. Yes, because car buyers of every brand were equally represented in the sample.
d. No, because every possible 400-buyer sample did not have an equal chance of being chosen.

e. No, because the population consisted of purchasers of four different brands of car.

7. A statistical analyst obtains data about ankle injuries by examining a hospital's records from the past 3 years.
a. Observational/Retrospective
b. Experiment/Retrospective
c. Observational/Prospective

d. Experiment/Prospective

8. An education researcher randomly selects 48 middle schools and interviews all the teachers at each school.
a. Systematic
b. Stratified
c. Random
d. Convenience
e. Cluster