A problem with a telephone line that prevents a customer from receiving or makin
ID: 3180952 • Letter: A
Question
A problem with a telephone line that prevents a customer from receiving or making calls is upsetting to both the customer and the telecommunications company. The accompanying table contains samples of 20 problems reported to two different offices of a telecommunications company and the time to clear these problems (in minutes) from the customers' lines. Complete parts (a) through (d) below.
Time
Location
1.28
1
1.93
1
0.82
1
2.62
1
0.51
1
1.53
1
4.57
1
3.68
1
1.35
1
3.62
1
1.15
1
0.58
1
0.82
1
1.52
1
0.75
1
1.16
1
6.43
1
3.84
1
5.25
1
0.88
1
8.38
2
3.56
2
0.09
2
1.29
2
0.66
2
0.45
2
3.59
2
2.16
2
0.51
2
3.36
2
3.63
2
0.71
2
1.87
2
0.58
2
1.31
2
4.02
2
0.06
2
1.23
2
1.77
2
0.63
2
a. At the 0.10 level of significance, is there evidence of a difference in the variability of the time to clear problems between the two central offices?
Determine the hypotheses, where sigma Subscript Upper A Superscript 2
is the population variance of the time to clear problems for office 1 and
sigma Subscript Upper B Superscript 2 is the population variance of the time to clear problems for office 2. Choose the correct answer below.
A.
H0: sigma Subscript Upper A Superscript 2 less than or equals sigma Subscript Upper B Superscript 2
H1: sigma Subscript Upper A Superscript 2 greater thansigma Subscript Upper B Superscript 2
B.
H0: sigma Subscript Upper A Superscript 2 greater than or equals sigma Subscript Upper B Superscript 2
H1: sigma Subscript Upper A Superscript 2 less thansigma Subscript Upper B Superscript 2
C.
H0: sigma Subscript Upper A Superscript 2 not equalssigma Subscript Upper B Superscript 2
H1: sigma Subscript Upper A Superscript 2 equalssigma Subscript Upper B Superscript 2
D.
H0: sigma Subscript Upper A Superscript 2 equals sigma Subscript Upper B Superscript 2
H1: sigma Subscript Upper A Superscript 2 not equals sigma Subscript Upper B Superscript 2
Compute the FSTAT test statistic.
FSTAT equals ____
(Round to three decimal places as needed.)
Determine the critical value.
The critical value is ____
(Round to three decimal places as needed.)
State the conclusion.
Reject / Do Not Reject H0. There is Insufficient / Sufficient evidence to support the claim that the variabilities of the time to clear problems between the two central offices are different.
b. Find the p-value.
The p-value is ____
(Round to three decimal places as needed.)
What does the p-value mean?
The probability of obtaining samples that give rise to a test statistic
Less than or equal to / greater than or equal to the negative of the critical value / critical value / negative of the test statistic / test statistic , found previously, is equal to the p-value if the population variances of the time to clear problems for both offices are the same.
c. What assumption needs to be made in (a) about the two populations in order to justify the use of the F test?
A. The samples are taken from populations that have the same mean.
B. Each of the two populations is normally distributed.
C. The populations do not contain any outliers.
D. The samples are taken from populations that have the same variance.
E. The samples are taken from populations that are independent and identically distributed.
F. There is enough information given that no assumptions need to be made.
d. Based on the results of (a) and (b), which t test should be used to compare the mean time to clear problems in the two central offices? Choose the correct answer below.
A. A pooled dash variance t test should be used because the test of hypothesis indicated that the population variances of the times for the offices are equal.
B. A separate dash variance t test should be used because the test of hypothesis indicated that the population variances of the times for the offices are not equal.
C. A separate dash variance t test should be used because the test of hypothesis indicated that the population variances of the times for the offices are equal.
D. A pooled dash variance t test should be used because the test of hypothesis indicated that the population variances of the times for the offices are not equal.
Time
Location
1.28
1
1.93
1
0.82
1
2.62
1
0.51
1
1.53
1
4.57
1
3.68
1
1.35
1
3.62
1
1.15
1
0.58
1
0.82
1
1.52
1
0.75
1
1.16
1
6.43
1
3.84
1
5.25
1
0.88
1
8.38
2
3.56
2
0.09
2
1.29
2
0.66
2
0.45
2
3.59
2
2.16
2
0.51
2
3.36
2
3.63
2
0.71
2
1.87
2
0.58
2
1.31
2
4.02
2
0.06
2
1.23
2
1.77
2
0.63
2
Explanation / Answer
Answer:
a. At the 0.10 level of significance, is there evidence of a difference in the variability of the time to clear problems between the two central offices?
Determine the hypotheses, where sigma Subscript Upper A Superscript 2
is the population variance of the time to clear problems for office 1 and
sigma Subscript Upper B Superscript 2 is the population variance of the time to clear problems for office 2. Choose the correct answer below.
Answer: D.H0: sigma Subscript Upper A Superscript 2 equals sigma Subscript Upper B Superscript 2
H1: sigma Subscript Upper A Superscript 2 not equals sigma Subscript Upper B Superscript 2
Compute the FSTAT test statistic.
FSTAT equals 1.304
(Round to three decimal places as needed.)
Determine the critical value.
The critical value is 2.168
(Round to three decimal places as needed.)
State the conclusion.
Do Not Reject H0. There is Insufficient evidence to support the claim that the variabilities of the time to clear problems between the two central offices are different.
b. Find the p-value.
The p-value is 0.569
(Round to three decimal places as needed.)
What does the p-value mean?
The probability of obtaining samples that give rise to a test statistic
greater than or equal to the test statistic , found previously, is equal to the p-value if the population variances of the time to clear problems for both offices are the same.
c. What assumption needs to be made in (a) about the two populations in order to justify the use of the F test?
B. Each of the two populations is normally distributed.
C. The populations do not contain any outliers.
E. The samples are taken from populations that are independent and identically distributed.
d. Based on the results of (a) and (b), which t test should be used to compare the mean time to clear problems in the two central offices? Choose the correct answer below.
A. A pooled dash variance t test should be used because the test of hypothesis indicated that the population variances of the times for the offices are equal.
F Test for Differences in Two Variances
Data
Level of Significance
0.1
Larger-Variance Sample
Sample Size
20
Sample Variance
3.9636
Smaller-Variance Sample
Sample Size
20
Sample Variance
3.0396
Intermediate Calculations
F Test Statistic
1.3040
Population 1 Sample Degrees of Freedom
19
Population 2 Sample Degrees of Freedom
19
Two-Tail Test
Upper Critical Value
2.1683
p-Value
0.5686
Do not reject the null hypothesis
F Test for Differences in Two Variances
Data
Level of Significance
0.1
Larger-Variance Sample
Sample Size
20
Sample Variance
3.9636
Smaller-Variance Sample
Sample Size
20
Sample Variance
3.0396
Intermediate Calculations
F Test Statistic
1.3040
Population 1 Sample Degrees of Freedom
19
Population 2 Sample Degrees of Freedom
19
Two-Tail Test
Upper Critical Value
2.1683
p-Value
0.5686
Do not reject the null hypothesis
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.