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.