The owner of a comedy club has historically based her business decisions on the average age of her customers being 30 years. A random sample of the customers’ ages is shown below. Based on this sample, is the average age greater than 30 years? Use a 5% level of significance. Assume that the distribution of ages is approximately normal.

37     30     26     35     45     42     51     40

43     27     39     38     46     21     28     20

a) State the null and alternate hypotheses and the level of significance. Is the test left-tailed, right-tailed, or two-tailed?

b) Identify the appropriate sampling distribution: the standard normal for the student’s t. What is the value of the sample statistic?

c) Find (or estimate) the P-value. Sketch the sample distribution and show the area corresponding to the P-value.

d) Find the critical value(s).

e) Based on your answers for part (a) through (d), will you reject or fail to reject the null hypothesis? Interpret your conclusion in the context of the application.