Question

express the confidence interval (0.432, 0.52) in the form p ± e.
o a. 0.432 ± 0.088
o b. 0.476 ± 0.088
o c. 0.476 ± 0.044
o d. 0.432 ± 0.044

Explanation:

Step1: Calculate the margin of error \(E\)

The formula for the margin of error \(E\) in a confidence interval \((a,b)\) is \(E=\frac{b - a}{2}\). Here \(a = 0.432\) and \(b=0.52\). So \(E=\frac{0.52-0.432}{2}\).

$$E=\frac{0.088}{2}=0.044$$

Step2: Find the sample proportion \(\hat{p}\)

The formula for the sample proportion \(\hat{p}\) in a confidence interval \((a,b)\) is \(\hat{p}=\frac{a + b}{2}\). Substituting \(a = 0.432\) and \(b = 0.52\) gives \(\hat{p}=\frac{0.432+0.52}{2}\).

$$\hat{p}=\frac{0.952}{2}=0.476$$

Answer:

C. \(0.476\pm0.044\)