Chapter 8.5, Problem 61PB

Bootstrap interval for the mean In 2014, the General Social Survey interviewed 1399 randomly selected U.S. residents about how much time per week they spent surfing the web. The responses revealed a very right-skewed distribution, with a sample mean of 12 hours and a standard deviation of 15 hours, indicating that the population distribution is very far from normal. Should we be worried that one of the assumptions for using the t confidence interval from Section 8.3 for the population mean is violated? Let’s find the bootstrap confidence interval for the population mean. The data from the survey are available from the book’s website under the name “wwwhours”.

1. a. Draw a histogram and find the sample mean and median time people spent surfing the web per week
2. b. Find a 95% confidence interval for the mean time using the t interval from Section 8.3.
3. c. Explain the steps of how you would obtain a 95 % bootstrap confidence interval for the mean time.
4. d. Use the Bootstrap web app mentioned in Activity 3 or other software to find the 95% bootstrap confidence interval for the mean. (If you are using the web app, you can open the dataset in a spreadsheet and then copy and paste the values for the variable “hours” into the text field of the web app.)
5. e. The results from both approaches are virtually identical. Look at the bootstrap distribution of $\bar{x}$ displayed in the web app or other software. Is it surprising that it looks approximately normal? What theorem predicted this shape?