Question

express the confidence interval 0.111 < p < 0.555 in the form \hat{p} \pm e. \hat{p} \pm e = \square \pm \square

Explanation:

Step1: Calculate the point estimate $\hat{p}$

The point estimate $\hat{p}$ is the mid - point of the confidence interval. Use the formula $\hat{p}=\frac{\text{lower limit}+\text{upper limit}}{2}$.
Here, the lower limit $L = 0.111$ and the upper limit $U=0.555$.
So, $\hat{p}=\frac{0.111 + 0.555}{2}=\frac{0.666}{2}=0.333$.

Step2: Calculate the margin of error $E$

The margin of error $E$ is the distance from the point estimate to either the lower or upper limit. Use the formula $E=\frac{\text{upper limit}-\text{lower limit}}{2}$.
$E=\frac{0.555 - 0.111}{2}=\frac{0.444}{2}=0.222$.

Answer:

$\hat{p}\pm E=0.333\pm0.222$