Question

express the confidence interval ( 0.333 < p < 0.999 ) in the form ( hat{p}pm e ).
( hat{p}pm e=squarepmsquare )

Explanation:

Step1: Calculate the sample proportion $\hat{p}$

The sample proportion $\hat{p}$ is the mid - point of the confidence interval.
$$\hat{p}=\frac{0.333 + 0.999}{2}=\frac{1.332}{2}=0.666$$

Step2: Calculate the margin of error $E$

The margin of error $E$ is the distance from the mid - point to either end of the interval.
$$E=\frac{0.999-0.333}{2}=\frac{0.666}{2}=0.333$$

Answer:

$\hat{p}\pm E = 0.666\pm0.333$