Donald believes that western commuters drive an average of 10 miles more per day than eastern commuters do. He selects random samples from each group. The western mean is 23.5 miles, and the eastern mean is 19.4 miles. A 95 percent confidence interval to estimate the difference in population means, in miles, is (2.5,5.7). Which of the following statements is supported by the interval?

a) The probability that Donald is correct is 0.05 because 10 is not contained in the interval.

b) The probability that Donald is correct is 0.95 because 10 is not contained in the interval.

c) Donald is likely to be correct because the difference in the sample means (23.5-19.4=4.1) is contained in the interval.

d) Donald is likely to be incorrect because 10 is not contained in the interval.

e) Donald is likely to be incorrect because the difference in the sample means was 23.5-19.4=4.1 miles.

Question

Mathematics

Aldo

8 March, 18:11

Donald believes that western commuters drive an average of 10 miles more per day than eastern commuters do. He selects random samples from each group. The western mean is 23.5 miles, and the eastern mean is 19.4 miles. A 95 percent confidence interval to estimate the difference in population means, in miles, is (2.5,5.7). Which of the following statements is supported by the interval?

a) The probability that Donald is correct is 0.05 because 10 is not contained in the interval.

b) The probability that Donald is correct is 0.95 because 10 is not contained in the interval.

c) Donald is likely to be correct because the difference in the sample means (23.5-19.4=4.1) is contained in the interval.

d) Donald is likely to be incorrect because 10 is not contained in the interval.

e) Donald is likely to be incorrect because the difference in the sample means was 23.5-19.4=4.1 miles.

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Answers (1)

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Josh Tate · Answer 1

d) Donald is likely to be incorrect because 10 is not contained in the interval.

Explanation:

A confidence interval is an estimation of a confidence interval with a range of values which may contain parameters of population. This therefore means that, a 95 percent confidence interval to estimate the difference in population means, in miles, of (2.5,5.7) is a range with 2.5 being the lower bound and 5.7 the upper bound.

Since, Donald believes that western commuters drive an average of 10 miles more per day than eastern commuters do. Then we are supposed to have 10 within the range of value in the interval Since the range is from 2.5 to 5.7, Donald is, therefore, likely to be incorrect because 10 is not contained in the interval.