Question

use the given confidence interval to find the margin of error and the sample proportion. (0.743,0.769) 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.
$$\hat{p}=\frac{0.743 + 0.769}{2}=\frac{1.512}{2}=0.756$$

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 $0.769−0.743 = 0.026$.
$$E=\frac{0.769 - 0.743}{2}=\frac{0.026}{2}=0.013$$

Answer:

The margin of error $E = 0.013$