8. (4 points total, see point distributions below) The General Social Survey (GSS) is a survey of approximately 2000 adults conducted each year since 1972, for a total of more than 38,000 participants. During several years of the GSS, participants were asked how many close friends they have. The mean for this variable is 7.44 friends, with a standard deviation of 10.98. The median is 5.00 and the mode is 4.00.

a. (0.5) Are these data for a distribution of scores or a distribution of means? Explain.

b. (0.5) What do the mean and standard deviation suggest about the shape of the distribution? (Hint: Compare the sizes of the mean and the standard deviation.) What do the three measures of central tendency suggest about the shape of the distribution?

c. (0.5) Let's say that these data represent the entire population. Pretend that you randomly selected a person from this population and asked how many close friends she or he had. Would you compare this person to a distribution of scores or to a distribution of means? Explain your answer.

d. (1) Imagine that you randomly selected one person from this population who reported that he had 18 close friends. What is his z score? Based on this z score, what is his approximate percentile? Does it make sense to calculate a percentile for this person?

e. (0.5) Now pretend that you randomly selected a sample of 80 people from this population. Would you compare this sample to a distribution of scores or to a distribution of means? Explain your answer.

f. (1) Calculate the standard error and z statistic for the sample of 80 if their mean is 8.7. Based on this z statistic, what is the approximate percentile for this sample? Does it make sense to calculate a percentile for this sample? Explain your answer.