Question

use the given confidence interval to find the margin of error and the sample proportion. (0.721,0.749) e = (type an integer or a decimal.)

Explanation:

Step1: Find the sample proportion

The sample proportion $\hat{p}$ is the mid - point of the confidence interval.
$$\hat{p}=\frac{0.721 + 0.749}{2}=\frac{1.47}{2}=0.735$$

Step2: Find the margin of error

The margin of error $E$ is half of the length of the confidence interval.
The length of the confidence interval is $0.749−0.721 = 0.028$.
$$E=\frac{0.749 - 0.721}{2}=\frac{0.028}{2}=0.014$$

Answer:

$E = 0.014$