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 0.9 hours. A random sample of 15 deliveries yielded a sample mean delivery time of 3.2 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. (a) What is the test statistic? Round your answer to two decimal places. ANSWER: (b) What is the p-value of the test? Round your answer to four decimal places. ANSWER: (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.

Answer 1

a)

The null and alternate hypothesis are:

H0: $\mu=3$

Ha: $\mu>3$

The test statistic is given by:

$z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{3.2-3}{\frac{0.9}{\sqrt{15}}}=0.86$

b)

Since this is a right-tailed test, so the p-value is given by:

$P(Z>0.86)=1-P(Z<0.86)=1-0.80511=0.19489\approx 0.1949$

c)

Since p-value is greater than 0.05, so we do not have sufficient evidence to reject the null hypothesis H0.

Thus, do not reject the null hypothesis.

d)

Since p-value is greater than 0.01, so we do not have sufficient evidence to reject the null hypothesis H0.

Thus, do not reject the null hypothesis.