Question: The owner of a local nightclub has recently surveyed a random sample of 50 customers of the club. She would like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years.

a) What is the right test to perform? What are the null and alternative hypotheses of the test?

b) If she wants to be 95% confident in her decision, what rejection region should she use? What conclusion can she make?

c) What is the p-value associated with the test statistic?