SECTION 3.1 Exercises

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For Exercises 3.1 to 3.4, see page 124; for 3.5, see page 126; for 3.6, see page 126; and for 3.7 and 3.8, see page 127.

In several of the following exercises, you are asked to identify the type of data that is described. Possible answers include anecdotal data, available data, observational data that are from sample surveys, observational data that are not from sample surveys, and experiments. It is possible for some data to be classified in more than one category.

Question 3.9

3.9 A dissatisfied customer.

You like to eat tuna sandwiches. Recently you noticed that there does not seem to be as much tuna as you expected when you opened the can. Identify the type of data that this represents, and describe how it can or cannot be used to reach a conclusion about the amount of tuna in the cans.

3.9

This is anecdotal. You have just noticed that the can seems lacking and there are no real data to support the claim. If you wanted to collect data to test your theory you could measure the contents of a random sample.

Question 3.10

3.10 Claims settled for $3,300,000!

According to a story in Consumer Reports, three major producers of canned tuna agreed to pay $3,300,000 to settle claims in California that the amount of tuna in their cans was less than the amount printed on the label of the cans.6 What kind of data do you think was used in this situation to convince the producers to pay this amount of money to settle the claims? Explain your answer fully.

Question 3.11

3.11 Marketing milk.

An advertising campaign was developed to promote the consumption of milk by adolescents. Part of the campaign was based on a study conducted to determine the effect of additional milk in the diet of adolescents over a period of 18 months. A control group received no extra milk. Growth rates of total body bone mineral content (TBBMC) over the study period were calculated for each subject. Data for the control group were used to examine the relationship between growth rate of TBBMC and age.

  1. How would you classify the data used to evaluate the effect of the additional milk in the diet? Explain your answer.
  2. How would you classify the control group data on growth rate of TBBMC and age for the study of this relationship? Explain your answer.
  3. Can you classify the growth rate of TBBMC and age variables as explanatory or response? If so, which is the explanatory variable? Give reasons for your answer.

3.11

(a) This is an experiment. Groups were chosen to receive extra milk or not. (b) The control group data alone are observational because there was no treatment imposed of additional milk. (c) TBBMC is the response. Age is not the explanatory variable; it functions as a control variable. The treatment of “additional milk” is the explanatory variable.

Question 3.12

3.12 Satisfaction with allocation of concert tickets.

Your college sponsored a concert that sold out.

  1. After the concert, an article in the student newspaper reported interviews with three students who were unable to get tickets and were very upset with that fact. What kind of data does this represent? Explain your answer.
  2. A week later, the student organization that sponsored the concert set up a website where students could rank their satisfaction with the way that the tickets were allocated using a 5-point scale with values “very satisfied,” “satisfied,” “neither satisfied nor unsatisfied,” “dissatisfied,” and “very dissatisfied.” The website was open to any students who chose to provide their opinion. How would you classify these data? Give reasons for your answer.
  3. Suppose that the website in part (b) was changed so that only a sample of students from the college were invited by text message to respond, and those who did not respond within three days were sent an additional text message reminding them to respond. How would your answer to part (b) change, if at all?
  4. Write a short summary contrasting different types of data using your answers to parts (a), (b), and (c) of this exercise.

Question 3.13

3.13 Gender and consumer choices.

Men and women differ in their choices for many product categories. Are there gender differences in preferences for health insurance plans as well? A market researcher interviews a large sample of consumers, both men and women. She asks each consumer which of two health plans he or she prefers. Is this study an experiment? Why or why not? What are the explanatory and response variables?

3.13

This study is not an experiment because no treatment was imposed. The explanatory variable is gender; the response is the choice of health plan.

Question 3.14

3.14 Is the product effective?

An educational software company wants to compare the effectiveness of its computer animation for teaching about supply, demand, and market clearing with that of a textbook presentation. The company tests the economic knowledge of 50 first-year college students, then divides them into two groups. One group uses the animation, and the other studies the text. The company retests all the students and compares the increase in economic understanding in the two groups. Is this an experiment? Why or why not? What are the explanatory and response variables?

Question 3.15

3.15 Does job training work?

A state institutes a job-training program for manufacturing workers who lose their jobs. After five years, the state reviews how well the program works. Critics claim that because the state’s unemployment rate for manufacturing workers was 6% when the program began and 10% five years later, the program is ineffective. Explain why higher unemployment does not necessarily mean that the training program failed. In particular, identify some lurking variables (see page 118 in Chapter 2) whose effect on unemployment may be confounded with the effect of the training program.

3.15

The economy likely plays a large role in the unemployment rate, separate from the success of the training program. Other things like population size and other demographic information could play a role as well.

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Question 3.16

3.16 Are there treatments?

Refer to Exercises 3.9 through 3.15. For any of these that involve an experiment, describe the treatment that is used.