Question

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

Explanation:

Step1: Calculate the point estimate \(\hat{p}\)

The point estimate \(\hat{p}\) is the mid - point of the confidence interval. The formula for the mid - point of an interval \((a,b)\) is \(\hat{p}=\frac{a + b}{2}\).
Here \(a = 0.432\) and \(b=0.52\), so \(\hat{p}=\frac{0.432 + 0.52}{2}=\frac{0.952}{2}=0.476\).

Step2: Calculate the margin of error \(E\)

The margin of error \(E\) is the distance from the mid - point to either end of the interval. The formula is \(E=\frac{b - a}{2}\).
Substitute \(a = 0.432\) and \(b = 0.52\) into the formula: \(E=\frac{0.52-0.432}{2}=\frac{0.088}{2}=0.044\).

Answer:

B. \(0.476\pm0.044\)