Question

Researchers study the mean weight (in pounds) of adults between the ages of 30-40. The researchers form a SRS of adults and build a 90% confidence interval: [160, 180]. Which of the following statements are true about this confidence interval?

a. 90% of intervals built according to the method capture the true mean weight of adults between the ages of 30-40.
b. The intervals margin of error is 20.
c. There is a 90% chance that the mean weight of adults between the ages of 30- 40 is between 160 and 180 pounds.
d. The sample mean used to build this interval was 170 pounds.

Answer 1

d. The sample mean used to build this interval was 170 pounds.

Explanation:

Confidence interval concepts:

A confidence interval has two bounds, a lower bound and an upper bound.

A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.

The margin of error is the difference between the two bounds, divided by 2.

In this question:

Bounds 160 and 180, so the sample mean used was (160+180)/2 = 170, and thus the correct answer is given by option d.