3. The Metropolitan Bus Company claims that the mean waiting time for a bus during rush hour is less than 5 minutes. A random sample of 20 waiting times has a mean of 4.2 minutes with a standard deviation of 2.1 minutes. a) The sample mean is 4.2. Before doing any work, what is gut feeling about the chances of the population mean being less than or equal to 5? Do you think that the sample mean of 4.2 is low enough and provides enough evidence?

b) Which will you use to perform the hypothesis test, a z-test or t-test? Explain why.

c) At = 0.01, test the bus company's claim. Assume the distribution is normally distributed. d) Complete the hypothesis test and compare your results with your guess in part a.