Question

use the given confidence interval to find the margin of error and the sample proportion. (0.590, 0.620) e = 0.015 (type an integer or a decimal.) \hat{p}= (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.
The formula for the mid - point of an interval $(a,b)$ is $\hat{p}=\frac{a + b}{2}$.
Here, $a = 0.590$ and $b=0.620$.
So, $\hat{p}=\frac{0.590+0.620}{2}$.

Step2: Calculate the value of $\hat{p}$

$\hat{p}=\frac{0.590 + 0.620}{2}=\frac{1.21}{2}=0.605$.

Answer:

$\hat{p}=0.605$