A population proportion is to be estimated. Estimate the minimum sample size needed to achieve the specified margin of error with a 95% degree of confidence.
-A researcher wishes to estimate the proportion of children in a certain neighborhood who are living with only one parent. She wishes to achieve a margin of error of E = 0.021. What is the minimum sample size needed?
A)1134
B)48
C)4536
D)2268

Question

Quizplus · Accepted Answer

To find the minimum sample size needed, use the formula for sample size in estimating a population proportion: n = (Z^2 * p * (1-p)) / E^2. With a 95% confidence level, Z is approximately 1.96. Assuming maximum variability (p = 0.5), the formula becomes n = (1.96^2 * 0.5 * 0.5) / 0.021^2, which calculates to approximately 2268.

A Population Proportion Is to Be Estimated