Question

Hannah claims that people who live in southern states spend 9 hours more per week outside than do people in northern states. She selects a random sample from each group. The mean number of hours per week that people in southern states spent outside is 18.6, and the mean number of hours per week that people in northern states spent outside is 14.4. A 99% confidence interval to estimate the difference in population means (southern minus northern) is (0.4,8.0)(0.4,8.0).

1. Which of the following statements about Hannah’s claim is supported by the interval?

A. Hannah is likely to be incorrect because the difference in the sample means was 18.6 - 14.4 = 4.218.6 - 14.4 = 4.2 hours.
B. Hannah is likely to be incorrect because 9 is not contained in the interval.
C. The probability that Hannah is correct is 0.99 because 9 is not contained in the interval.
D. The probability that Hannah is correct is 0.01 because 9 is not contained in the interval.
E. Hannah is likely to be correct because the difference in the sample means (18.6 - 14.4 = 4.2)(18.6 - 14.4 = 4.2) is contained in the interval.

Answer 1

B. Hannah is likely to be incorrect because 9 is not contained in the interval.

Explanation:

She construct a 99% confidence interval for the difference between means and gets the interval (0.4, 8.0).

This means that there is 99% confidence that the true difference between means is within this interval.

The left 1% corresponds to the tails of the distribution: there is 0.5% probability that the difference between means is below 0.4 and 0.5% probability that the difference between means is above 8.0.

As she claims that 9 hours is the true difference, we can say that there is less than 0.5% that she is correct. In others words, is likely to be incorrect.