Question

question 8 of 10
a 98% confidence interval for a proportion is found to be (0.72, 0.78). what is
the margin of error?
a. 0.04
b. 0.02
c. 0.06
d. 0.03

Explanation:

Step1: Find the mid - point of the confidence interval

The mid - point of the confidence interval \((a,b)\) is \(\hat{p}=\frac{a + b}{2}\). Here \(a = 0.72\) and \(b=0.78\), so \(\hat{p}=\frac{0.72 + 0.78}{2}=\frac{1.5}{2}=0.75\).

Step2: Calculate the margin of error

The margin of error \(E\) is given by \(E=b-\hat{p}\) (or \(E=\hat{p}-a\)). Using \(b = 0.78\) and \(\hat{p}=0.75\), we get \(E=0.78 - 0.75=0.03\).

Answer:

D. 0.03