At Harvard, it is widely accepted that the average age of MBA students is 36. You think it must be higher than that, and you set up a hypothesis test to see if you are right. You survey 20 people in your program and the ages in your sample are as follows: 26, 27, 30, 32, 33, 34, 35, 36, 37, 39, 40, 42, 43, 45, 48, 52, 53, 56, 59, 60. Conduct a hypothesis test using a 5% level of significance to determine if the MBA student age mean is more than 36 years.
a. What are you null and alternative hypotheses?
b. Can you reject the null? What is your rationale?
c. What does the 5% significance level mean? Be specific.
d. What would a Type I or Type II error mean in the context of this problem?