Question: Consider the following scenario:

Dr. Jeffrey M. Barrett of Lakeland, Florida, reported data on eight cases of umbilical cord prolapse. The maternal ages were 25, 28, 17, 26, 27, 22, 25, and 30. He was interested in determining if he could conclude that the mean age of the population of his sample was greater than 20 years. Let \(\alpha \) = 0.01.

The null and alternative hypotheses for this problem are defined as:

Ho: \(\mu \) = 20 and Ha: \(\mu \) > 20

a. Explain the meaning of a Type I error in the context of this problem.

b. Explain the meaning of a Type II error in the context of this problem.

c. Suppose Dr. Barrett expanded his study to include a total of 50 subjects and then calculated a test statistic of z = 2.33 for his hypothesis test. What is the associated p-value? What is the conclusion for this test?