Question

1. “Fana Lube” is a regional chain that provides a standard service for performing oil changes and basic checkups on automobiles. The chain has a standard that says the average time per car for this service should be 15 minutes. There is considerable variability in times due to differences in layout of engines, degree of time pressure from other jobs, and many other sources. As a result, the management of the chain decided to study if the standard is being met and randomly selected 30 oil change and basic checkup services within a month and carefully recorded the time they took in minutes. The resulting data are reported in the following table.

13.7	11	19	20.5	12.9	14.6	15.7	10.7	15.8	37.6	26.6	14.6	15.5	14.8	18.9
18.2	18	12	11.5	12.6	16.6	19.8	16.2	15.3	15.3	22.3	24.7	10.8	30.8	14.9

1. Using the given data, please construct the 90% and the 99% confidence intervals for the mean time it takes to complete oil change and basic checkup services at Fana Lube. Clearly show all the necessary steps and interpret your result. Based on your results would you conclude that the chain is achieving its stated standard? Please justify your answer.                                                                      [4points]
2. What is the probability that the mean time for oil change and basic checkup services at Fana Lube could be greater than the upper limit of the 90% confidence interval?  Also explain which confidence interval is wider and why. What do you think will happen to the confidence intervals if the sample size is increased to 50? Please justify your answers.                                                                    [2 points]
3. Using the given data and at 1% level of significance, please test whether the chain is achieving its stated standard for the average time for oil change and basic checkup services. Show the necessary steps and explain your conclusion. Is your test result consistent with the conclusion you arrived at based on the 99% confidence interval you constructed under question (a) above? Please explain.         [4 points]

Answer 1