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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Exhibit 4 (Questions 19-22)
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
Refer to Exhibit 4. Assuming that the
population of service times follows an approximately normal
distribution, what...

The manager of the service department of a local car dealership
has noted that the service times of a sample of 15 new automobiles
have a sample variance of S2 = 16.
A 95% confidence interval estimate for the population variance
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A 95% confidence interval estimate for the population
standard deviation of service times for all their new
automobiles is:

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HA: σ2 ≠ 210
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a. s2= 281; n =
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0.05 p-value < 0.10
0.02 p-value < 0.05
0.01 p-value < 0.02
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