Question

use the given confidence interval to find the margin of error and the sample p(0.761,0.787)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, $a = 0.761$ and $b=0.787$.
So, $\hat{p}=\frac{0.761+0.787}{2}$.

Step2: Simplify the expression

$\hat{p}=\frac{1.548}{2}=0.774$.

Answer:

$\hat{p}=0.774$