Question

7. You wish to test the conventional wisdom that the average age of an American voter is 49. You randomly select n = 36 voters, and find a sample mean of 53 with a sample standard deviation of 12.

a. Conduct a two-tailed hypothesis test using significance level ? = .05. Clearly state the hypotheses, the test statistic, the p-value, and your conclusion.

b. Construct a 95% confidence interval, and explain how the confidence interval confirms your results from part a.

c. Replicate the hypothesis test and construction of the confidence interval in part a and part b assuming instead that the sample size is n=25 (keeping all other information the same).

You are interested in evaluating whether 25 percent of Americans have a bachelor’s degree or higher (conventional wisdom). You survey n = 100 Americans, and find that 22 had a bachelor’s degree or higher.

a. Conduct a two-tailed hypothesis test using significance level ? = .05. Clearly state the hypotheses, the test statistic, the p-value, and your conclusion.

b. Construct a 95% confidence interval for the proportion of Americans with a bachelor’s degree or higher.

Answer 1