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 value of \(\hat{p}\)

The formula for \(\hat{p}\) in the confidence interval \(a < p< b\) is \(\hat{p}=\frac{a + b}{2}\). Here \(a = 0.222\) and \(b=0.444\), so \(\hat{p}=\frac{0.222+0.444}{2}=\frac{0.666}{2}=0.333\).

Step2: Calculate the value of \(E\)

The formula for \(E\) in the confidence interval \(a < p< b\) is \(E=\frac{b - a}{2}\). Substitute \(a = 0.222\) and \(b = 0.444\) into the formula, we get \(E=\frac{0.444-0.222}{2}=\frac{0.222}{2}=0.111\).

Answer:

\(\hat{p}\pm E=0.333\pm0.111\)