The 2008 GSS of the American adult population found a mean age of 39.2 and a standard deviation of 17.35 for a selected sample of 400 adults. Assume that we know from census data that the mean age of all American adults is 37.7. Use this information to answer the following question. Show your work in as much detail as possible. i. One-tailed test a. State the research and the null hypotheses in statistical notation. b. Calculate the t statistic and test the null hypothesis at the .05 significance level. c. Do you reject the null hypothesis? d. What conclusion(s) do you draw as a result of the hypothesis test?