One of the questions asked of a random sample of adult Americans on the 2004 General Social Survey (GSS) was:

From time to time, most people discuss important matters with other people. Looking back over the last six months— who are the people with whom you discussed matters important to you? Just tell me their first names or initials.
The interviewer then recorded how many names each person gave. The GSS is a survey of a representative sample of U.S. adults who are not institutionalized. There were 1467 responses, and the average number of close friends reported was 1.987, with a standard deviation of 1.771. Th e data are not strongly skewed.
a. Explain how you know from the sample average and sample standard deviation that the distribution of number of close friends people tend to report is not bell-shaped.
b. In the context of this study, explain why it is valid to use the theory-based (t-distribution) approach to find a confidence interval?

c. Use the Theory-Based Inference applet to find and report a 99% confidence interval for the parameter of interest. Also, interpret the interval in the context of the study.
d. Based on the above 99% confidence interval alone, is there evidence that the average number of close friends people tend to report is different from 2? How are you deciding?