7.28 Number of friends on Facebook. To mark Facebook’s 10th birthday, Pew Research surveyed people using Facebook to see what they like and dislike about the site. The survey found that among adult Facebook users, the average number of friends is 338. This distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right with a median of 200 friends.11 Consider the following SRS of Facebook users from your large university.

107 246 289 177 155 101 80 461 336 78
463 264 827 180 221 1065 79 691 70 921
126 672 296 60 11 227 84 787 18 82

  1. (a) Are these data also heavily skewed? Use graphical methods to examine the distribution. Write a short summary of your findings.

  2. (b) Do you think it is appropriate to use the t methods of this section to compute a 95% confidence interval for the mean number of friends that Facebook users at your large university have? Explain why or why not.

  3. (c) Compute the sample mean and standard deviation, the standard error of the mean, and the margin of error for 95% confidence.

  4. (d) Report the 95% confidence interval for μ, the average number of friends for Facebook users at your large university.