Question

express the confidence interval ( 0.111 < p < 0.333 ) in the form ( hat{p} pm e ). ( hat{p} pm e=square pm square )

Explanation:

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

The formula for $\hat{p}$ is $\hat{p}=\frac{\text{lower limit}+\text{upper limit}}{2}$.
Substitute the lower limit $0.111$ and upper limit $0.333$:
$\hat{p}=\frac{0.111 + 0.333}{2}=\frac{0.444}{2}=0.222$

Step2: Calculate the margin of error $E$

The formula for $E$ is $E=\frac{\text{upper limit}-\text{lower limit}}{2}$.
Substitute the lower limit $0.111$ and upper limit $0.333$:
$E=\frac{0.333 - 0.111}{2}=\frac{0.222}{2}=0.111$

Answer:

$0.222\pm0.111$