Question

use the given confidence interval to find the margin of error and the sample proportion. (0.590,0.620) 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.
$$\hat{p}=\frac{0.590 + 0.620}{2}=\frac{1.21}{2}=0.605$$

Step2: Find the margin of error

The margin of error $E$ is the distance from the sample proportion to either end of the confidence interval.
$$E=0.620-\hat{p}$$
Substitute $\hat{p} = 0.605$ into the formula:
$$E=0.620 - 0.605=0.015$$

Answer:

$E = 0.015$