Question: A commuter railroad advertises that their trains have an average on-time arrival record of exactly 85 percent. A transportation analyst conducts a study to determine if this claim is true. He checks arrival performance for a sample of 64 commuter trains and finds that the average on-time arrival rate is 83 percent. It is known that the population standard deviation is 5 percent. Test the hypothesis that the commuter railroad’s claim is true at a = 0.05.

a. State the null and alternative hypothesis.

b. Determine the critical value of the statistic.

c. Write the decision rule.

d. Calculate the sample test statistic.

e. Perform the test.

f. Write a conclusion based on your answer to part e.