A sample of 82 Oscar winning actresses had a mean age of 35.9 years and standard deviation 11.1 years when winning Oscars. Use a 0.05 significance level to test the claim that the mean age of actresses when they win Oscars is less than 38 years.

a. State the hypotheses and identify the claim.

b. Find the test statistic and p-value.

c. State your conclusion.

d. Find a confidence interval comparable to the hypothesis test for the mean age of actresses when they win Oscars