Question

use the given confidence interval to find the margin of error and the sample proportion. (0.761,0.787) e = (type an integer or a decimal.)

Explanation:

Step1: Calculate the sample proportion

The sample proportion $\hat{p}$ is the mid - point of the confidence interval.
$$\hat{p}=\frac{0.761 + 0.787}{2}=\frac{1.548}{2}=0.774$$

Step2: Calculate the margin of error

The margin of error $E$ is half of the width of the confidence interval.
$$E=\frac{0.787 - 0.761}{2}=\frac{0.026}{2}=0.013$$

Answer:

$E = 0.013$