Question

nutes 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.
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

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.
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.  

Answer 1

Answer:

Explained below.

Step-by-step explanation:

(1)

The hypothesis can be defined as follows:

H₀: The Speedy Oil Change will change the oil in​ customers’ cars in more than 30 minutes on average, i.e. μ > 30.

Hₐ: The Speedy Oil Change will change the oil in​ customers’ cars in less than 30 minutes on average, i.e. μ ≤ 30.

(2)

Use Excel to compute the sample mean and standard deviation as follows:

$\bar x=\text{AVERAGE(array)}=24.917\\\\s=\text{STDEV.S(array)}=8.683$

Compute the test statistic as follows:

$t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{24.917-30}{8.683/\sqrt{36}}=-3.51$

The degrees of freedom is:

df = n - 1

   = 36 - 1

   = 35

Compute the p-value as follows:

$p-value=P(t_{35}$

(3)

The p-value = 0.0006 is very small.

The null hypothesis will be rejected at any of the commonly used significance level.

(4)

There is sufficient evidence to support the claim that the Speedy Oil Change will change the oil in​ customers’ cars in less than 30 minutes on average.