Question

A car dealer ship randomly selected 40 clients ( from their thousands of clients) to determine the average time it took them to sell them a car. They found that on average the clients on this sample stayed 135.7 minutes from when the client entered the dealership to when the client drove off in their new car with standard deviation of 47.3 minutes. Is the average time the clients spend in dealership for all the clients more than 2.5 hours?

a. Perform a hypothesis test to answer your professor:

i. Write the hypotheses. (10 pts)

ii. Explicitly check conditions (and assumptions) and calculate the appropriate test statics. (complete the problem even if the conditions not met). (16pts)

iii. Using a significance level of 0.05, determine the results of the hypothesis test and explicitly answer the question posed in the problem. (10pts)

b. Construct 99% confidence interval for the average time clients spends buying a car in the dealership and interpret the interval. ( check conditions as needed). (16pts)

Answer 1