Question

express the confidence interval ( 0.333 < p < 0.777 ) 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 midpoint of the confidence interval.

$$ \hat{p}=\frac{0.333 + 0.777}{2}=\frac{1.11}{2}=0.555 $$

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.

$$ E=\hat{p}-0.333=0.555 - 0.333=0.222 $$

Answer:

\(0.555\pm0.222\)