Chapter 11.6, Problem 77E

As part of a study described in the report “I Can’t Get My Work Done!” (harmon.ie/blog/i-cant-get-my-work-done-how-collaboration-social-tools-drain- productivity, 2011, retrieved May 6, 2017), people in a sample of 258 cell phone users age 20 to 39 were asked if they use their cell phones to stay connected while they are in bed, and 168 said “yes.” The same question was also asked of each person in a sample of 129 cell phone users age 40 to 49, and 61 said “yes.” We might expect the proportion who stay connected while in bed to be higher for the 20 to 39 age group than for the 40 to 49 age group, but how much higher?

1. a. Construct and interpret a 90% large-sample confidence interval for the difference in the population proportions of cell phone users age 20 to 39 and those age 40 to 49 who say that they sleep with their cell phones. Interpret the confidence interval in context.
2. b. Note that the sample sizes in the two groups—cell phone users age 20 to 39 and those age 40 to 49—are large enough to satisfy the conditions for a large-sample test and a large-sample confidence interval for two population proportions. Even though the sample sizes are large enough, simulation-based methods can still be used. Use the output at the bottom of the page to identify a 90% bootstrap confidence interval for the difference in the population proportions of cell phone users age 20 to 39 and those age 40 to 49 who say that they sleep with their cell phones.
3. c. Compare the confidence intervals calculated in Parts (a) and (b). Would the interpretation change using the bootstrap confidence interval compared with the large-sample confidence interval? Explain.