1. Explain why both of the situations in Activity 8.1 and Activity 8.2 are observational experiments. What key elements of a designed experiment are missing in each situation?

2. A movie company wishes to measure the effect of advertising on box office receipts. Thirty U.S. cities with similar demographics are chosen for an experiment. The 30 cities are randomly divided into three groups of 10 cities. In each city a trailer for a new film will be run on a local cable station during prime time in the week leading up to the release of the film. In the first group of 10 cities the trailer will be run 500 times, in the second group the trailer will be run 1,000 times, and in the third group it will be run 1,500 times. The company will collect the box office receipts for the opening weekend of the film in each city and compare the mean box office receipts.

Explain why this is a designed experiment. Identify the factor and the response variable. Is the factor quantitative or qualitative? Identify the factor levels and the experimental units. What part of choosing the cities is not necessarily random? Explain why it might be difficult to randomize this part of the experiment.

3. Suppose Bank of America wants to determine whether e-mail and postcard reminders of the benefits of the Keep the Change program result in customers using their debit cards more often. A random sample of customers is chosen and split into four groups. The customers in one group are sent an e-mail reminder, those in the second group are sent a postcard, the customers in the third group are sent both, and those in the last group are sent neither. The bank keeps track of how many more times each customer uses his/her debit card in the 2 weeks after the reminders are sent as compared to the 2 weeks before the reminders are sent. The means for the four groups are compared.

Explain why this is a designed experiment. Identify the factors and the response variable. Is the factor quantitative or qualitative? Identify the factor levels, the treatments, and the experimental units. Comparing this experiment with that in Exercise 2, why is it more realistic to choose a random sample for the experiment?

4. For each of the designed experiments in Exercises 2 and 3, rework the experiment to have a randomized block design. Explain how you will choose your experimental units from each population. Then describe the criteria you would use to split the experimental units into matched sets. How do you determine which experimental unit in each matched set receives each level of treatment? What data are collected and how are the data compared? Do you believe that there is any benefit to the block design?

Explain.

Activity 8.1

Use the Internet to find the daily box office receipts for two different hit movies during the first 8 weeks after their releases. In this activity, you will compare the mean daily box office receipts of these movies in two different ways.

1. Independently select random samples of size n = 30 from the data sets for each of the movies’ daily box office receipts. Find the mean and standard deviation of each sample. Then find a confidence interval for the difference of the means.

2. Now pair the data for the two movies by day, that is, the box office receipts for the day of release for each movie are paired, the box office receipts for each movie’s second day are paired, and so forth. Calculate the difference in box office receipts for each day and select a random sample of size n = 30 from the daily differences. Then find a confidence interval for the sample mean.

3. Explain how the sampling for the paired difference experiment is different from the independent sampling. How might this sampling technique yield a better comparison of the two means in the box office example?

4. Compute the actual means for the daily box office receipts for each of the movies and then find the difference of the means. Does the difference of the means lie in both confidence intervals you found? Is the exact difference remarkably closer to one of the estimates? Explain.

Activity 8.2

In this activity, you will compare the mean amounts transferred for two different Bank of America customers as well as design some studies that might help the marketing department determine where to allocate more of its advertising budget.

1. You will need to work with another student in the class on this exercise. Each of you should use your data set Amounts Transferred from the Chapter 1 Activity as a random sample from a theoretically larger set of all your amounts ever transferred. Then the means and standard deviations of your data sets will be the sample means and standard deviations. Write a confidence interval for the difference of the two means at the 95% level. Does the interval contain 0? Are your mean amounts transferred significantly different? Explain.

2. Design a study to determine whether there is a significant difference in the mean amount of Bank of America matches for customers in California enrolled in the program and the mean amount of Bank of America matches for customers in Florida enrolled in the program. Be specific about sample sizes, tests used, and how a conclusion will be reached. How might the results of this study help Bank of America estimate costs in the program?

3. Design a study to determine whether there is a significant difference in the percentage of Bank of America customers in California enrolled in the program and the percentage of Bank of America customers in Florida enrolled in the program.

Be specific about sample sizes, tests used, and how a conclusion will be reached. How might the results of this study help Bank of America’s marketing department?

Keep the results from this activity for use in other activities.