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 percent confidence interval to estimate the difference in population means (southern minus northern) is (0.4,8.0).

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:

Hello!

Hannah estimated per CI the difference between the average time that people spend outside in southern states and the average time people spend outside in northern states.

The CI is a method of estimation of population parameters that propose a range of possible values for them. The confidence level you use to construct the interval can be interpreted as, if you were to calculate 100 confidence interval, you'd expect that 99 of them will contain the true value of the parameter of interest.

In this example, the 99%CI resulted [0.4;8.0]hs

Meaning that with a 99% confidence level you'd expect the value of the difference between the average time people from southern states spend outside than the average time people from northern states spend outside is included in the interval [0.4;8.0]hs.

Now, she claims that people living in southern states spend 9 more hours outside than people living in northern states, symbolized μ₁ - μ₂ > 9

Keep in mind that if you were to test her claim, the resulting hypothesis test would be one-tailed

H₀: μ₁ - μ₂ ≤ 9

H₁: μ₁ - μ₂ > 9

And that the calculated Ci is tow-tailed, so it is not valid to use it to decide over the hypotheses pair. This said, considering that the calculated interval doesn't contain 9, it is most likely that Hannah's claim is incorrect.

I hope this helps!