Question

question 7 of 10
suppose that, based on a sample, the 68% confidence interval for the mean
of a population is (63, 75). what was the mean of the sample?

a. 73
b. 69
c. 77
d. 81

Explanation:

Step1: Recall the formula for confidence interval

The confidence interval for the mean is given by \(\bar{x}-E<\mu <\bar{x} + E\), where \(\bar{x}\) is the sample mean and \(E\) is the margin of error. The mid - point of the confidence interval \((a,b)\) is the sample mean \(\bar{x}=\frac{a + b}{2}\).

Step2: Calculate the sample mean

Here, \(a = 63\) and \(b=75\). Then \(\bar{x}=\frac{63 + 75}{2}=\frac{138}{2}=69\).

Answer:

B. 69