Question

express the confidence interval ( 0.444 < p < 0.888 ) in the form ( hat{p}pm e ).

( hat{p}pm e=squarepmsquare )

Explanation:

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

The point estimate $\hat{p}$ is the midpoint of the confidence interval. Use the formula $\hat{p}=\frac{\text{lower limit}+\text{upper limit}}{2}$.
Here, the lower limit is $0.444$ and the upper limit is $0.888$. So, $\hat{p}=\frac{0.444 + 0.888}{2}=\frac{1.332}{2}=0.666$.

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: $E=\frac{0.888 - 0.444}{2}=\frac{0.444}{2}=0.222$.

Answer:

$0.666\pm0.222$