MATH 1342 Name ___________________________ Elementary Statistical Methods COAT Assessment - Ch.10 - Hypothesis Testing One Sample Empirical/Quantitative Skills 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 population mean oil change time is less than 30 minutes at a significance level of 0.01. 1. Write the null and alternative hypothesis. Label each accordingly. 2. Calculate the Test Statistic and the P-value. Label each accordingly, and report the P-value to 4 decimal places. 3. Using the P-value calculated in #2, explain why you would or would not reject the null hypothesis? Answer using a complete sentence, proper grammar and correct spelling. Do NOT write a conclusion. Lab Ch.9-10 continued 4. Based on your answer to #3, write a final conclusion for the test of hypotheses, and explain if the company is fulfilling its promise to \"change the oil in customers' cars in less than 30 minutes on average?\" Answer using a complete sentence, proper grammar and correct spelling. Unfortunately, Speedy Oil Change continues to get customer complaints. As the manager, you feel that perhaps more analysis is needed. 5. Construct a 98% confidence interval for the mean oil change time. (Round to 1 decimal place) 6. Using the above interval, state the point estimate and calculate the margin of error for the interval. (1 decimal place) Point Estimate = _______ minutes Margin of Error = _______ minutes 7. Write a sentence that interprets the confidence interval. Answer using a complete sentence, proper grammar and correct spelling. 8. To fully address customer complaints, you also investigate the time needed to complete each individual oil change. a. How many of the 36 oil changes took longer than 30 minutes? b. Should the company continue using the mean oil change time in their advertisements? Justify your answer using a complete sentence, proper grammar and correct spelling