Question

question 1 of 10
a 98% confidence interval for a proportion is found to be (0.72, 0.78). what is the sample proportion?

a. 0.74
b. 0.78
c. 0.75
d. 0.76

Explanation:

Step1: Recall confidence interval for proportion

The confidence interval for a proportion is given by \(\hat{p} \pm E\), where \(\hat{p}\) is the sample proportion and \(E\) is the margin of error. This means the interval is \((\hat{p} - E, \hat{p} + E)\). The sample proportion \(\hat{p}\) is the midpoint of the interval.

Step2: Calculate the midpoint

To find the midpoint of the interval \((0.72, 0.78)\), we use the formula for the midpoint of two numbers \(a\) and \(b\): \(\frac{a + b}{2}\).

Substituting \(a = 0.72\) and \(b = 0.78\) into the formula:

$$ \hat{p}=\frac{0.72 + 0.78}{2}=\frac{1.5}{2} = 0.75 $$

Answer:

C. 0.75