Question

Exhibit 4
The manager of the service department of a local car dealership has noted that the service times of a sample of 15 new automobiles has a sample standard deviation of S = 4 hours. We are interested to test the following hypotheses using α = 0.05 level of significance:
                                              H0 : σ2 ≤ 14
                                              Ha : σ2 > 14

a. Refer to Exhibit 4. Assuming that the population of service times follows an approximately normal distribution, what is the value of the test statistic?

A. 4
B. 14
C. 15
D. 16

b. Refer to Exhibit 4. Assuming that the population of service times follows an approximately normal distribution, what is the p-value?

A. More than 0.10
B. Between 0.05 and 0.10  
C. Less than 0.01
D. between 0.025 and 0.05

c. Refer to Exhibit 4. Assuming that the population of service times follows an approximately normal distribution, what is the conclusion?

A. Reject the null hypothesis at  α = 0.05 . The sample supports the alternative hypothesis that the population variance of the service times exceeds 14.
B. We cannot reject the null hypothesis at  α = 0.05 . The sample does not support the alternative hypothesis that the population variance of the service times exceeds 14.
C. We can reject the null hypothesis only if the level of significance, α,  is reduced from 0.05  to 0.01.
D. The test is inconclusive.

Answer 1

Answer:

As the population of service times follows an approximately normal distribution, the propoer test statistic is Chi Square with degree of freedom = 15-1 = 14

a) Test statistic is,

= 16

b) P-value = P( > 16) =  0.3134

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no sufficient evidence that population variance is greater than 14 hours.

c)

Reject the null hypothesis at  α = 0.05 . The sample supports the alternative hypothesis that the population variance of the service times exceeds 14.

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