Question

express the confidence interval ( 0.222 < p < 0.888 ) 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 $U=0.888$. So, $\hat{p}=\frac{0.222 + 0.888}{2}=\frac{1.11}{2}=0.555$.

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 $E=\frac{\text{upper limit}-\text{lower limit}}{2}$.
Substitute the values: $E=\frac{0.888 - 0.222}{2}=\frac{0.666}{2}=0.333$.

Answer:

$0.555\pm0.333$