One way to check on how representative a survey is of the population from which it was drawn is to compare various characteristics of the sample with the population characteristics. A typical variable used for this purpose is age. The 2010 GSS of the American adult population found a mean age of 49.28 and a standard deviation of 17.21 for its sample of 4,857 adults. Assume that we know from census data that the mean age of all American adults is 37.2. Use this information to answer these questions.
a. State the research and the null hypotheses for a two-tailed test.
b. Calculate the t statistic and test the null hypothesis at the .001 significance level. What did you find?
c. What is your decision about the null hypothesis? What does this tell us about how representative the sample is of the American adult population?