Question

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 23 19 11 10 27
41 27 22 26 24 32
27 25 25 35 31 22
23 31 17 37 33 25
28 24 28 21 40 16
33 30 14 23 22 10

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?"

Answer 1

Based on the mean time calculated from the sample, Speedy Oil Change is fulfilling its promise to change oil in less than 30 minutes on average. The sample's mean time for oil changes is approximately 25.1 minutes, which supports the company's claim.

Step-by-step explanation:

To investigate the complaints at Speedy Oil Change, we start by calculating the mean time for the 36 randomly audited oil changes. We need to add all the times together and then divide by the number of observations (36).

The sum of the recorded times is: 42 + 23 + 19 + 11 + 10 + 27 + 41 + 27 + 22 + 26 + 24 + 32 + 27 + 25 + 25 + 35 + 31 + 22 + 23 + 31 + 17 + 37 + 33 + 25 + 28 + 24 + 28 + 21 + 40 + 16 + 33 + 30 + 14 + 23 + 22 + 10 = 902 minutes.

The mean time is 902 minutes divided by 36 oil changes which equals approximately 25.1 minutes per oil change.

Based on this sample, it appears that Speedy Oil Change is fulfilling its promise to change the oil in customers' cars in less than 30 minutes on average. However, the presence of some times above 30 minutes indicates variability in service times that could lead to customer complaints. Further analysis could include calculating the standard deviation to assess this variability.