A large online store prides itself on its fast response to email questions to its technical department. A recent sample of 19 sample emails showed that the mean time for the technical department to respond was 36.00 hours with a standard deviation of 3.00 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 37.84 hours. At the 0.025 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: < 37.84

H₁: 37.84H₀: 37.84

H₁: < 37.84H₀: = 37.84

H₁: 37.84

b)We will use thet-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 thez-statistic because of the results of the central limit theorem.

c)What is the critical value oft?

For full marks, your answer should be accurate to three decimal places.

Critical value:

0

d)Draw your conclusion for this one-sample test.Do not reject H₀.Reject H₀and accept H₁.We do not have enough information to decide.