whether pairs of observations are dependent or not

Question

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Answer 1

Question

Chapter 10.5, Problem 10.39E

(a)

To determine

To explain: whether pairs of observations are dependent or not

(a)

Expert Solution

Answer to Problem 10.39E

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Conclusion: Thus, the given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

(b)

To determine

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

(b)

Expert Solution

Answer to Problem 10.39E

There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differs by 0.01 level of significance.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

Here we have to test the difference of the means of the GEICO and 21^s^t Century annual premiums.

Under this the null and alternative hypothesis are defined as follows:

H0:μd=0

VsHa:μd≠0

To test the null hypothesis by using the MINITAB

We have the output as follows

Paired T-Test and CI: GEICO, 21^s^tCentury

Sample	N	Mean	StDev	SE Mean
GEICO	4	2428.75	244.48	122.24
21^s^t Century	4	2404.50	106.34	53.17
Difference	4	24.2500	288.6813	144.3407

99% CI for mean difference:(−818.8308,867.3308)

T-Test of difference=0 (vs not=):T-Value=0.17 P−Value=0.877

From the above output the test statistics value is tSTAT=0.17 .

The critical value for the test is at 0.01 level of significance and at 6 degrees of freedom is 3.71.

The calculated value does not lie in the critical region we fail to reject the null hypothesis and there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Conclusion: There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

(c)

To determine

To find: the approximate p-value for the test and interpret its value.

(c)

Expert Solution

Answer to Problem 10.39E

The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The P-value from the MINITAB output is given by P(T≤t)=0.877 .

The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Conclusion: The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

(d)

To determine

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

(d)

Expert Solution

Answer to Problem 10.39E

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance is given by d¯±tα/2(sdn)

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Conclusion: From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

(e)

To determine

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

(e)

Expert Solution

Answer to Problem 10.39E

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

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Answer 2

Question

Chapter 10.5, Problem 10.39E

(a)

To determine

To explain: whether pairs of observations are dependent or not

(a)

Expert Solution

Answer to Problem 10.39E

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Conclusion: Thus, the given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

(b)

To determine

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

(b)

Expert Solution

Answer to Problem 10.39E

There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differs by 0.01 level of significance.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

Here we have to test the difference of the means of the GEICO and 21^s^t Century annual premiums.

Under this the null and alternative hypothesis are defined as follows:

H0:μd=0

VsHa:μd≠0

To test the null hypothesis by using the MINITAB

We have the output as follows

Paired T-Test and CI: GEICO, 21^s^tCentury

Sample	N	Mean	StDev	SE Mean
GEICO	4	2428.75	244.48	122.24
21^s^t Century	4	2404.50	106.34	53.17
Difference	4	24.2500	288.6813	144.3407

99% CI for mean difference:(−818.8308,867.3308)

T-Test of difference=0 (vs not=):T-Value=0.17 P−Value=0.877

From the above output the test statistics value is tSTAT=0.17 .

The critical value for the test is at 0.01 level of significance and at 6 degrees of freedom is 3.71.

The calculated value does not lie in the critical region we fail to reject the null hypothesis and there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Conclusion: There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

(c)

To determine

To find: the approximate p-value for the test and interpret its value.

(c)

Expert Solution

Answer to Problem 10.39E

The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The P-value from the MINITAB output is given by P(T≤t)=0.877 .

The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Conclusion: The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

(d)

To determine

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

(d)

Expert Solution

Answer to Problem 10.39E

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance is given by d¯±tα/2(sdn)

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Conclusion: From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

(e)

To determine

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

(e)

Expert Solution

Answer to Problem 10.39E

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

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Answer 3

Question

Chapter 10.5, Problem 10.39E

(a)

To determine

To explain: whether pairs of observations are dependent or not

(a)

Expert Solution

Answer to Problem 10.39E

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Conclusion: Thus, the given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

(b)

To determine

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

(b)

Expert Solution

Answer to Problem 10.39E

There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differs by 0.01 level of significance.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

Here we have to test the difference of the means of the GEICO and 21^s^t Century annual premiums.

Under this the null and alternative hypothesis are defined as follows:

H0:μd=0

VsHa:μd≠0

To test the null hypothesis by using the MINITAB

We have the output as follows

Paired T-Test and CI: GEICO, 21^s^tCentury

Sample	N	Mean	StDev	SE Mean
GEICO	4	2428.75	244.48	122.24
21^s^t Century	4	2404.50	106.34	53.17
Difference	4	24.2500	288.6813	144.3407

99% CI for mean difference:(−818.8308,867.3308)

T-Test of difference=0 (vs not=):T-Value=0.17 P−Value=0.877

From the above output the test statistics value is tSTAT=0.17 .

The critical value for the test is at 0.01 level of significance and at 6 degrees of freedom is 3.71.

The calculated value does not lie in the critical region we fail to reject the null hypothesis and there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Conclusion: There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

(c)

To determine

To find: the approximate p-value for the test and interpret its value.

(c)

Expert Solution

Answer to Problem 10.39E

The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The P-value from the MINITAB output is given by P(T≤t)=0.877 .

The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Conclusion: The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

(d)

To determine

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

(d)

Expert Solution

Answer to Problem 10.39E

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance is given by d¯±tα/2(sdn)

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Conclusion: From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

(e)

To determine

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

(e)

Expert Solution

Answer to Problem 10.39E

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

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Answer 4

Question

Chapter 10.5, Problem 10.39E

(a)

To determine

To explain: whether pairs of observations are dependent or not

(a)

Expert Solution

Answer to Problem 10.39E

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Conclusion: Thus, the given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

(b)

To determine

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

(b)

Expert Solution

Answer to Problem 10.39E

There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differs by 0.01 level of significance.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

Here we have to test the difference of the means of the GEICO and 21^s^t Century annual premiums.

Under this the null and alternative hypothesis are defined as follows:

H0:μd=0

VsHa:μd≠0

To test the null hypothesis by using the MINITAB

We have the output as follows

Paired T-Test and CI: GEICO, 21^s^tCentury

Sample	N	Mean	StDev	SE Mean
GEICO	4	2428.75	244.48	122.24
21^s^t Century	4	2404.50	106.34	53.17
Difference	4	24.2500	288.6813	144.3407

99% CI for mean difference:(−818.8308,867.3308)

T-Test of difference=0 (vs not=):T-Value=0.17 P−Value=0.877

From the above output the test statistics value is tSTAT=0.17 .

The critical value for the test is at 0.01 level of significance and at 6 degrees of freedom is 3.71.

The calculated value does not lie in the critical region we fail to reject the null hypothesis and there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Conclusion: There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

(c)

To determine

To find: the approximate p-value for the test and interpret its value.

(c)

Expert Solution

Answer to Problem 10.39E

The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The P-value from the MINITAB output is given by P(T≤t)=0.877 .

The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Conclusion: The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

(d)

To determine

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

(d)

Expert Solution

Answer to Problem 10.39E

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance is given by d¯±tα/2(sdn)

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Conclusion: From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

(e)

To determine

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

(e)

Expert Solution

Answer to Problem 10.39E

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

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Answer 5

Chapter 10.5, Problem 10.39E

(a)

To determine

To explain: whether pairs of observations are dependent or not

(a)

Expert Solution

Answer to Problem 10.39E

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Conclusion: Thus, the given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

(b)

To determine

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

(b)

Expert Solution

Answer to Problem 10.39E

There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differs by 0.01 level of significance.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

Here we have to test the difference of the means of the GEICO and 21^s^t Century annual premiums.

Under this the null and alternative hypothesis are defined as follows:

H0:μd=0

VsHa:μd≠0

To test the null hypothesis by using the MINITAB

We have the output as follows

Paired T-Test and CI: GEICO, 21^s^tCentury

Sample	N	Mean	StDev	SE Mean
GEICO	4	2428.75	244.48	122.24
21^s^t Century	4	2404.50	106.34	53.17
Difference	4	24.2500	288.6813	144.3407

99% CI for mean difference:(−818.8308,867.3308)

T-Test of difference=0 (vs not=):T-Value=0.17 P−Value=0.877

From the above output the test statistics value is tSTAT=0.17 .

The critical value for the test is at 0.01 level of significance and at 6 degrees of freedom is 3.71.

The calculated value does not lie in the critical region we fail to reject the null hypothesis and there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Conclusion: There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

(c)

To determine

To find: the approximate p-value for the test and interpret its value.

(c)

Expert Solution

Answer to Problem 10.39E

The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The P-value from the MINITAB output is given by P(T≤t)=0.877 .

The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Conclusion: The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

(d)

To determine

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

(d)

Expert Solution

Answer to Problem 10.39E

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance is given by d¯±tα/2(sdn)

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Conclusion: From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

(e)

To determine

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

(e)

Expert Solution

Answer to Problem 10.39E

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Answer 6

Chapter 10.5, Problem 10.39E

(a)

To determine

To explain: whether pairs of observations are dependent or not

(a)

Expert Solution

Answer to Problem 10.39E

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Conclusion: Thus, the given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Answer 7

Chapter 10.5, Problem 10.39E

(a)

To determine

To explain: whether pairs of observations are dependent or not

Answer 8

(a)

Expert Solution

Answer to Problem 10.39E

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Conclusion: Thus, the given pair of observations is not dependent since the annual premiums of the GEICO are not dependent on the annual premiums of the 21^s^t Century so the given pair of observations is not dependent.

Answer 13

(b)

To determine

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

(b)

Expert Solution

Answer to Problem 10.39E

There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differs by 0.01 level of significance.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

Here we have to test the difference of the means of the GEICO and 21^s^t Century annual premiums.

Under this the null and alternative hypothesis are defined as follows:

H0:μd=0

VsHa:μd≠0

To test the null hypothesis by using the MINITAB

We have the output as follows

Paired T-Test and CI: GEICO, 21^s^tCentury

Sample	N	Mean	StDev	SE Mean
GEICO	4	2428.75	244.48	122.24
21^s^t Century	4	2404.50	106.34	53.17
Difference	4	24.2500	288.6813	144.3407

99% CI for mean difference:(−818.8308,867.3308)

T-Test of difference=0 (vs not=):T-Value=0.17 P−Value=0.877

From the above output the test statistics value is tSTAT=0.17 .

The critical value for the test is at 0.01 level of significance and at 6 degrees of freedom is 3.71.

The calculated value does not lie in the critical region we fail to reject the null hypothesis and there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Conclusion: There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Answer 14

(b)

To determine

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

Answer 15

(b)

Expert Solution

Answer to Problem 10.39E

There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differs by 0.01 level of significance.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

Here we have to test the difference of the means of the GEICO and 21^s^t Century annual premiums.

Under this the null and alternative hypothesis are defined as follows:

H0:μd=0

VsHa:μd≠0

To test the null hypothesis by using the MINITAB

We have the output as follows

Paired T-Test and CI: GEICO, 21^s^tCentury

Sample	N	Mean	StDev	SE Mean
GEICO	4	2428.75	244.48	122.24
21^s^t Century	4	2404.50	106.34	53.17
Difference	4	24.2500	288.6813	144.3407

99% CI for mean difference:(−818.8308,867.3308)

T-Test of difference=0 (vs not=):T-Value=0.17 P−Value=0.877

From the above output the test statistics value is tSTAT=0.17 .

The critical value for the test is at 0.01 level of significance and at 6 degrees of freedom is 3.71.

The calculated value does not lie in the critical region we fail to reject the null hypothesis and there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Conclusion: There is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums differ at 0.01 level of significance.

Answer 20

(c)

To determine

To find: the approximate p-value for the test and interpret its value.

(c)

Expert Solution

Answer to Problem 10.39E

The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The P-value from the MINITAB output is given by P(T≤t)=0.877 .

The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Conclusion: The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Answer 21

(c)

To determine

To find: the approximate p-value for the test and interpret its value.

Answer 22

(c)

Expert Solution

Answer to Problem 10.39E

The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The P-value from the MINITAB output is given by P(T≤t)=0.877 .

The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Conclusion: The P-value from the MINITAB output is given by P(T≤t)=0.877 . The P-value is greater than the level of significance 0.01 so there is no enough evidence to support the claim that the means of the GEICO and 21^s^t Century annual premiums are differ.

Answer 27

(d)

To determine

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

(d)

Expert Solution

Answer to Problem 10.39E

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance is given by d¯±tα/2(sdn)

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Conclusion: From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Answer 28

(d)

To determine

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

Answer 29

(d)

Expert Solution

Answer to Problem 10.39E

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Answer 30

(d)

Expert Solution

Answer 31

(d)

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

The 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance is given by d¯±tα/2(sdn)

From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Conclusion: From the MINITAB output the 99% confidence interval is (−818.8308,867.3308) .

Answer 34

(e)

To determine

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

(e)

Expert Solution

Answer to Problem 10.39E

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Answer 35

(e)

To determine

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

Answer 36

(e)

Expert Solution

Answer to Problem 10.39E

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Answer 37

(e)

Expert Solution

Answer 38

(e)

Expert Solution

Answer 39

Expert Solution

Answer 40

Explanation of Solution

Given:

City	GEICO ($)	21^s^tCentury ($)
Long Beach	2780	2352
Pomona	2411	2462
San Bernardino	2261	2284
Moreno Valley	2263	2520

Calculation:

By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21^s^t Century annual premiums throughout the United States.

Answer 41

Ch. 10.3 - Prob. 10.1E Ch. 10.3 - Prob. 10.2E Ch. 10.3 - Prob. 10.3E Ch. 10.3 - Prob. 10.4E Ch. 10.3 - Prob. 10.5E Ch. 10.3 - Prob. 10.6E Ch. 10.3 - Dissolved O2 Content Industrial wastes andsewage...Ch. 10.3 - Prob. 10.8E Ch. 10.3 - Prob. 10.10E Ch. 10.3 - Prob. 10.11E

whether pairs of observations are dependent or not

Concept explainers

Videos

To explain: whether pairs of observations are dependent or not

Answer to Problem 10.39E

Explanation of Solution

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

Answer to Problem 10.39E

Explanation of Solution

To find: the approximate p-value for the test and interpret its value.

Answer to Problem 10.39E

Explanation of Solution

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

Answer to Problem 10.39E

Explanation of Solution

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not

Answer to Problem 10.39E

Explanation of Solution

Want to see more full solutions like this?

Chapter 10 Solutions

whether pairs of observations are dependent or not

Concept explainers

Videos

To explain: whether pairs of observations are dependent or not

Answer to Problem 10.39E

Explanation of Solution

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21st Century insurance

Answer to Problem 10.39E

Explanation of Solution

To find: the approximate p-value for the test and interpret its value.

Answer to Problem 10.39E

Explanation of Solution

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21st Century insurance.

Answer to Problem 10.39E

Explanation of Solution

To explain:whether the comparisons between GEICO and 21st Century insuranceis made throughout the United States or not

Answer to Problem 10.39E

Explanation of Solution

Want to see more full solutions like this?

Chapter 10 Solutions

To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21^s^t Century insurance

To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21^s^t Century insurance.

To explain:whether the comparisons between GEICO and 21^s^t Century insuranceis made throughout the United States or not