Question

express the confidence interval 0.039 < p < 0.479 in the form p ± e.
a. 0.259 ± 0.44
b. 0.259 ± 0.5
c. 0.259 ± 0.22
d. 0.22 ± 0.5

Explanation:

Step1: Find the point estimate $\hat{p}$

The point estimate $\hat{p}$ is the mid - point of the confidence interval. We use the formula $\hat{p}=\frac{a + b}{2}$, where $a = 0.039$ and $b=0.479$. So, $\hat{p}=\frac{0.039 + 0.479}{2}=\frac{0.518}{2}=0.259$.

Step2: Find the margin of error $E$

The margin of error $E$ is half of the length of the confidence interval. The length of the confidence interval is $b - a$. So, $E=\frac{0.479 - 0.039}{2}=\frac{0.44}{2}=0.22$.

Answer:

C. $0.259\pm0.22$