A courier service advertises that its average delivery time is less than 3 hours for deliveries in the Vancouver area. The distribution of delivery times is known to be normal, with standard deviation hours. A random sample of deliveries yielded a sample mean delivery time of hours. Consider a test of the null hypothesis that the population mean is 3 against the one-sided alternative that the population mean delivery time is greater than 3. Answer the following, rounding your answers to three decimal places where appropriate.

(a) What is the test statistic?

(b) What is the p-value of the test?

(c) By interpreting the p-value in (b) can the null hypothesis be rejected at a 5% significant level?





(c) Can the null hypothesis be rejected at a 1% significant level?



You can earn partial credit on this problem.