Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that adresses the original claim. Use the P-value method.

Listed below are ages of actresses and actors from a country at the times that they won a certain award. The data are paired according to the years that they won. Use a 0.01 significance level to test the belief that best actresses are younger than best actors. Does the result suggest a problem in that culture? Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal.

Best Actresses 33, 29, 27, 27, 37, 41, 28, 38, 26, 21, 33, 42, 32, 30, 35

Best Actors 30, 41, 48, 52, 40, 39, 62, 34, 34, 62, 42, 56, 41, 33, 29