Drive safely: How often does the average driver have an accident? The Allstate Insurance Company determined the average number of years between accidents for drivers in a large number of U.S. cities. Following are the results for 32 cities east of the Mississippi River and 32 cities west of the Mississippi River.
- Construct a 95% confidence interval for the difference in
mean scores between western and eastern cities. - An insurance company executive claims that the mean number of years between accidents for western cities is 1.5 years greater than the mean for eastern cities. Does the confidence interval contradict this claim?
a.
To find: The
Answer to Problem 26E
The
Explanation of Solution
Given information:
The data is,
East | |||||||
10.2 | 9.5 | 11.2 | 1 1.4 | 9.8 | 10.0 | 11.6 | 1 0.7 |
9.5 | 9.0 | 7.2 | 11.5 | 7.7 | 9.0 | 8.9 | 8.4 |
6.8 | 5.3 | 8.0 | 8.8 | 9.0 | 10.0 | 9.7 | 11.6 |
7.9 | 9.9 | 10.5 | 11.9 | 10.9 | 8.6 | 6.7 | 9.6 |
West | |||||||
9.5 | 7.9 | 13.4 | 12.6 | 9.7 | 8.2 | 14.0 | 7.1 |
10.2 | 9.4 | 10.8 | 9.5 | 7.5 | 9.1 | 8.4 | 7.6 |
7.4 | 7.7 | 7.1 | 11.9 | 10.2 | 11.9 | 7.7 | 7.0 |
10.0 | 8.1 | 11.5 | 8.4 | 9.6 | 9.5 | 9.9 | 11.5 |
Concept used:
Minitab is used.
Calculation:
The steps for the confidence interval are,
Import the data, select start and choose the basic statistics option then select the 2 sample t and enter summarized data.
Click option button choose confidence level, test difference and alternative hypothesis and then click ok.
The data is shown below.
Figure-1
Therefore, the
b.
To find: Whether the confident interval contradict the claim.
Answer to Problem 26E
The confident interval contradicts the claim.
Explanation of Solution
Given information:
The data is,
East | |||||||
10.2 | 9.5 | 11.2 | 1 1.4 | 9.8 | 10.0 | 11.6 | 1 0.7 |
9.5 | 9.0 | 7.2 | 11.5 | 7.7 | 9.0 | 8.9 | 8.4 |
6.8 | 5.3 | 8.0 | 8.8 | 9.0 | 10.0 | 9.7 | 11.6 |
7.9 | 9.9 | 10.5 | 11.9 | 10.9 | 8.6 | 6.7 | 9.6 |
West | |||||||
9.5 | 7.9 | 13.4 | 12.6 | 9.7 | 8.2 | 14.0 | 7.1 |
10.2 | 9.4 | 10.8 | 9.5 | 7.5 | 9.1 | 8.4 | 7.6 |
7.4 | 7.7 | 7.1 | 11.9 | 10.2 | 11.9 | 7.7 | 7.0 |
10.0 | 8.1 | 11.5 | 8.4 | 9.6 | 9.5 | 9.9 | 11.5 |
Concept used:
Minitab is used.
Calculation:
Since, the
Therefore, the confident interval contradicts the claim.
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