6.56 Rural friendships and the General Social Survey: Earlier, we considered data from the GSS on numbers of close friends people reported having. The mean for this variable is 7.44, with a standard deviation of 10.98. Let’s say that you decide to use the GSS data to test whether people who live in rural areas have a different mean number of friends than does the overall GSS sample. Again, treat the overall GSS sample as the entire population of interest. Let’s say that you select 40 people living in rural areas and find that they have an average of 3.9 friends.

a. What is the independent variable in this study? Is this variable nominal, ordinal, or scale?

b. What is the dependent variable in this study? Is this variable nominal, ordinal, or scale?

c. What is the null hypothesis for this study?

d. What is the research hypothesis for this study?

e. Would we compare the sample data to a distribution of scores or to a distribution of means? Explain.

f. Using symbolic notation and formulas, calculate the mean and the standard error for the distribution of means. g. Using symbolic notation and the formula, calculate the z statistic for this sample.

h. What is the approximate percentile for this sample? i. Let’s say that the researchers concluded that people in rural areas have fewer friends than does the general population (thus rejecting the null hypothesis). If they are incorrect, have they made a Type I or a Type II error? Explain.