The U.S.Department of Health and Human Services collected sample data for 772 males between the ages of 18 and 24.That sample group has a mean height of 69.7 inches with a standard deviation of 2.8 inches.Find the 99% confidence interval for the mean height of all males between the ages of 18 and 24.
A)[63.19 76.21]
B)[62.49 76.91]
C)[69.65 69.75]
D)[69.47 69.93]
E)[69.44 69.96]

Question

Quizplus · Accepted Answer

To find the 99% confidence interval for the mean height of all males between the ages of 18 and 24, we will use the formula:

Confidence interval = sample mean ± (z-score) x (standard deviation of the sample mean)

Where the z-score corresponds to the level of confidence desired. Since we want a 99% confidence interval, the z-score will be 2.576 (from a Z-table or calculator).

Plugging in the numbers we have:

Confidence interval = 69.7 ± (2.576) x (2.8/√772)
Confidence interval = 69.7 ± 0.26
Confidence interval = [69.44, 69.96]

Therefore, the best choice is E.

The USDepartment of Health and Human Services Collected Sample Data for for 772