A courier service advertises that its average delivery time is less than 3 hours

Question

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 1.2 hours. A random sample of 15 deliveries yielded a sample mean delivery time of 3.36 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? A. Do not reject the null hypothesis. B. Reject the null hypothesis. (c) Can the null hypothesis be rejected at a 1% significant level? A. Do not reject the null hypothesis. B. Reject the null hypothesis.

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 3
HA : > 3
Standard deviation = 1.2

Hypothesis test results:

Hence,

a) Test statistic = 1.1619

b) p - Value = 0.1226

c) p - value > 0.05, do not reject the null hypothesis.

d) p - value > 0.01, do not reject the null hypothesis.

Mean n Sample Mean Std. Err. Z-Stat P-value 15 3.36 0.30983867 1.161895 0.1226

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