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?

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Answer 1

Textbook Question

Chapter 10.1, Problem 26E

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.

Chapter 10.1, Problem 26E, Drive safely: How often does the average driver have an accident? The Allstate Insurance Company

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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

a.

Expert Solution

To determine

To find: The 95% confidence interval for the difference in mean scores between western and eastern cities.

Answer to Problem 26E

The 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

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.

Elementary Statistics (Text Only), Chapter 10.1, Problem 26E

Figure-1

Therefore, the 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

b.

Expert Solution

To determine

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 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) and it does not include 1.5 .

Therefore, the confident interval contradicts the claim.

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Answer 2

Textbook Question

Chapter 10.1, Problem 26E

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.

Chapter 10.1, Problem 26E, Drive safely: How often does the average driver have an accident? The Allstate Insurance Company

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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

a.

Expert Solution

To determine

To find: The 95% confidence interval for the difference in mean scores between western and eastern cities.

Answer to Problem 26E

The 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

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.

Elementary Statistics (Text Only), Chapter 10.1, Problem 26E

Figure-1

Therefore, the 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

b.

Expert Solution

To determine

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 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) and it does not include 1.5 .

Therefore, the confident interval contradicts the claim.

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Answer 3

Textbook Question

Chapter 10.1, Problem 26E

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.

Chapter 10.1, Problem 26E, Drive safely: How often does the average driver have an accident? The Allstate Insurance Company

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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

a.

Expert Solution

To determine

To find: The 95% confidence interval for the difference in mean scores between western and eastern cities.

Answer to Problem 26E

The 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

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.

Elementary Statistics (Text Only), Chapter 10.1, Problem 26E

Figure-1

Therefore, the 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

b.

Expert Solution

To determine

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 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) and it does not include 1.5 .

Therefore, the confident interval contradicts the claim.

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Answer 4

Textbook Question

Chapter 10.1, Problem 26E

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.

Chapter 10.1, Problem 26E, Drive safely: How often does the average driver have an accident? The Allstate Insurance Company

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?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

a.

Expert Solution

To determine

To find: The 95% confidence interval for the difference in mean scores between western and eastern cities.

Answer to Problem 26E

The 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

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.

Elementary Statistics (Text Only), Chapter 10.1, Problem 26E

Figure-1

Therefore, the 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

b.

Expert Solution

To determine

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 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) and it does not include 1.5 .

Therefore, the confident interval contradicts the claim.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

To find: The 95% confidence interval for the difference in mean scores between western and eastern cities.

Answer to Problem 26E

The 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

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.

Elementary Statistics (Text Only), Chapter 10.1, Problem 26E

Figure-1

Therefore, the 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

b.

Expert Solution

To determine

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 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) and it does not include 1.5 .

Therefore, the confident interval contradicts the claim.

Answer 8

a.

Expert Solution

To determine

To find: The 95% confidence interval for the difference in mean scores between western and eastern cities.

Answer to Problem 26E

The 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

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.

Elementary Statistics (Text Only), Chapter 10.1, Problem 26E

Figure-1

Therefore, the 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

To find: The 95% confidence interval for the difference in mean scores between western and eastern cities.

Answer 13

Answer to Problem 26E

The 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

Answer 14

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.

Elementary Statistics (Text Only), Chapter 10.1, Problem 26E

Figure-1

Therefore, the 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) .

Answer 15

b.

Expert Solution

To determine

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 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) and it does not include 1.5 .

Therefore, the confident interval contradicts the claim.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

To find: Whether the confident interval contradict the claim.

Answer 20

Answer to Problem 26E

The confident interval contradicts the claim.

Answer 21

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 95% confidence interval for the difference in mean scores between western and eastern cities is (−0.773,0.992) and it does not include 1.5 .

Therefore, the confident interval contradicts the claim.

Answer 22

Ch. 10.1 - In Exercises 5 and 6, fill in each blank with e...Ch. 10.1 - In Exercises 5 and 6, fill in each blank with e...Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - In Exercises 9-14, construct the confidence...Ch. 10.1 - Prob. 10E Ch. 10.1 - In Exercises 9-14, construct the confidence...Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E

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Answer to Problem 26E

Explanation of Solution

Answer to Problem 26E

Explanation of Solution

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