Question

express the confidence interval (0.432, 0.52) in the form \\( \hat { p } \pm e \\).
a. \\( 0.476 \pm 0.044 \\)
b. \\( 0.432 \pm 0.088 \\)
c. \\( 0.476 \pm 0.088 \\)
d. \\( 0.432 \pm 0.044 \\)

Explanation:

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

The sample proportion $\hat{p}$ is the mid - point of the confidence interval.
$$\hat{p}=\frac{0.432 + 0.52}{2}=\frac{0.952}{2}=0.476$$

Step2: Calculate the margin of error $E$

The margin of error $E$ is the distance from the mid - point to either end of the confidence interval.
$$E=0.476-0.432 = 0.044$$

Answer:

A. $0.476\pm0.044$