Question

A large online store prides itself on its fast response to email questions to its technical department. A recent sample of 16 sample emails showed that the mean time for the technical department to respond was 46.00 hours with a standard deviation of 5.00 hours. The store has recently hired more staff members, and wants to know if the time to respond to emails has dropped from last year's average of 47.73 hours. At the 0.05 significance level, is it reasonable to conclude the average response time is less than last year's average? Follow the steps below to answer this question.

a)

Select the null and alternative hypotheses.

	H0: μ ≥ 47.73 H1: μ < 47.73
	H0: μ < 47.73 H1: μ ≥ 47.73
	H0: μ = 47.73 H1: μ ≠ 47.73

b)

We will use the t-statistic for this question, but is there another way? If any, what assumptions must we make?

	No, there is no other way in this instance, but we have to assume the population is normal.
	No, there is no other way in this instance, and we don't have to make any assumptions.
	Yes, there is another way. We could choose to use the z-statistic because of the results of the central limit theorem.

c) What is the critical value of t?
your answer should be accurate to three decimal places.

Critical value:___

d)

Draw your conclusion for this one-sample test.

	Do not reject H0.
	Reject H0 and accept H1.
	We do not have enough information to decide.

Answer 1