A 2018 General Social Survey (GSS) asked a random sample of 1,118 adult Americans how often they contacted their closest friend by either phone, internet, other communication device, or face to face. The GSS is a survey of a representative sample of U.S. adults who are not institutionalized. Of the 1,118 responses, the average number of times per week that the respondent contacted their closest friend was 2.87, with a standard deviation of 2.46. The data are not strongly skewed. 

a. Explain how you know from the sample average and sample standard deviation that the distribution of the number of times per week people contacted their close friends 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 99% confidence interval alone, is there evidence that the average number of times per week people contacted their close friends is different from 3? How are you deciding?