Question

use the given confidence interval to find the margin of error and the sample proportion. (0.752,0.778) e = 0.013 (type an integer or a decimal.) \hat{p}=\square (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.
The formula for the mid - point of an interval $(a,b)$ is $\hat{p}=\frac{a + b}{2}$.
Here, $a = 0.752$ and $b=0.778$.
So, $\hat{p}=\frac{0.752+0.778}{2}$.

Step2: Simplify the expression

First, add the values in the numerator: $0.752 + 0.778=1.53$.
Then, divide by 2: $\hat{p}=\frac{1.53}{2}=0.765$.

Answer:

$\hat{p}=0.765$