Suppose you are the manager of Speedy Oil Change which claims that it will change the oil in customers cars in less than 30 minutes on average.Further suppose that several complaints have been filed from customers stating that their oil change took longer than 30 minutes.Upper-level management at Speedy Oil Change headquarters has requested that you investigate the complaints.To begin your investigation, you randomly audit 36 oil changes performed by Speedy Oil Change and record the time each customer waited for the oil change.The number of minutes to complete each of the 36 oil changes is reported below.

42

29

19

11

10

27

41

27

22

26

28

32

17

15

25

35

31

22

13

31

17

37

33

25

18

24

28

21

40

19

33

30

14

23

22

10

(data from http://org.elon.edu/econ/sac/Descriptive.htm)

In the questions below, you will test if the mean is significantly less than 30 minutes at a significance level of 0.01.

1.List the requirements that should be met for this hypothesis test.

-Method of sampling is simple random sample

-The sample size here is 36 and that is greater than 30 so the sampling distribution is Normal

2.Write the null and alternative hypothesis.

-Hzero- u>=30,Hone- u<30

3.Calculate the test statistic and the P-value.Label each accordingly.

4.Would you reject the null hypothesis?Justify your answer using a complete sentence and proper

grammar.

5. Is the company fulfilling its promise to change the oil in customers cars in less than 30 minutes on

average?

Unfortunately, Speedy Oil Change continues to get customer complaints. As the manager, you feel that perhaps more analysis is needed.You know that you are likely to be asked how much less than 30 minutes is our mean oil change?

6.Construct a 98% confidence interval.Report this confidence interval accurate to 1 decimal place.

7.State the point estimate and calculate the margin of error.

8.Explain to your superiors how to interpret this interval.

9.Using the confidence interval you created, calculate the range of values that answers the question

how much less than 30 minutes is our mean oil change?

10.What other factors might you need to consider in order to address the customer complaints?