Question

express the confidence interval using the indicated format.

1. express the confidence interval 0.039 < p < 0.479 in the form of $hat{p}pm e$.

a) 0.259 $pm$ 0.22
b) 0.22 $pm$ 0.5
c) 0.259 $pm$ 0.5
d) 0.259 - 0.22

Explanation:

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

The point - estimate $\hat{p}$ is the mid - point of the confidence interval. The formula for $\hat{p}$ is $\hat{p}=\frac{\text{lower limit}+\text{upper limit}}{2}$. Given lower limit $L = 0.039$ and upper limit $U=0.479$, then $\hat{p}=\frac{0.039 + 0.479}{2}=\frac{0.518}{2}=0.259$.

Step2: Calculate the margin of error $E$

The margin of error $E$ is the distance from the point - estimate to either the lower or upper limit of the confidence interval. So $E=\hat{p}-L$ (or $E = U-\hat{p}$). Using $E=\hat{p}-L$, we have $E=0.259 - 0.039=0.22$.

Answer:

A. $0.259\pm0.22$