Concept explainers
(a)
To explain: whether pairs of observations are dependent or not
(a)
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 21st Century so the given pair of observations is not dependent.
Explanation of Solution
Given:
City | GEICO ($) | 21stCentury ($) |
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 21st 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 21st Century so the given pair of observations is not dependent.
(b)
To find: whether the given data is an evidence to indicate the difference in the average annual premiums between GEICO and 21st Century insurance
(b)
Answer to Problem 10.39E
There is no enough evidence to support the claim that the means of the GEICO and 21st Century annual premiums differs by 0.01 level of significance.
Explanation of Solution
Given:
City | GEICO ($) | 21stCentury ($) |
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 21st Century annual premiums.
Under this the null and alternative hypothesis are defined as follows:
Vs
To test the null hypothesis by using the MINITAB
We have the output as follows
Paired T-Test and CI: GEICO, 21stCentury
Sample | N | Mean | StDev | SE Mean |
GEICO | 4 | 2428.75 | 244.48 | 122.24 |
21st Century | 4 | 2404.50 | 106.34 | 53.17 |
Difference | 4 | 24.2500 | 288.6813 | 144.3407 |
From the above output the test statistics value is
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 21st 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 21st Century annual premiums differ at 0.01 level of significance.
(c)
To find: the approximate p-value for the test and interpret its value.
(c)
Answer to Problem 10.39E
The P-value from the MINITAB output is given by
Explanation of Solution
Given:
City | GEICO ($) | 21stCentury ($) |
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
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 21st Century annual premiums are differ.
Conclusion: The P-value from the MINITAB output is given by
(d)
To find: a 99% confidence interval for the difference in the average annual premiums for GEICO and 21st Century insurance.
(d)
Answer to Problem 10.39E
From the MINITAB output the 99% confidence interval is
Explanation of Solution
Given:
City | GEICO ($) | 21stCentury ($) |
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 21st Century insurance is given by
From the MINITAB output the 99% confidence interval is
Conclusion: From the MINITAB output the 99% confidence interval is
(e)
To explain:whether the comparisons between GEICO and 21st Century insuranceis made throughout the United States or not
(e)
Answer to Problem 10.39E
By using the given information it is not possible to compare the difference between GEICO and 21st Century annual premiums throughout the United States.
Explanation of Solution
Given:
City | GEICO ($) | 21stCentury ($) |
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 21st Century annual premiums throughout the United States.
Conclusion: By using the given information it is not possible to compare the difference between GEICO and 21st Century annual premiums throughout the United States.
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Chapter 10 Solutions
Introduction to Probability and Statistics
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