Question

express the confidence interval ( 0.222 < p < 0.444 ) 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 $L = 0.222$ and the upper limit $U=0.444$. So, $\hat{p}=\frac{0.222 + 0.444}{2}=\frac{0.666}{2}=0.333$.

Step2: Calculate the margin of error $E$

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

Answer:

$0.333\pm0.111$