According to a report in USA Today, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?
A) 1.645(0.0040)
B) 1.645(0.0632)
C) 1.96(0.0040)
D) 1.96(0.0632)

Question

Quizplus · Accepted Answer

The margin of error for a 95% confidence interval is calculated using the formula $Z \times \sqrt{\frac{p(1-p)}{n}}$, where $Z$ is the Z-score for the confidence level (1.96 for 95%), $p$ is the sample proportion, and $n$ is the sample size. Here, $p = \frac{8}{40} = 0.20$, so the margin of error is $1.96 \times \sqrt{\frac{0.20(1-0.20)}{40}} = 1.96(0.0632)$.

According to a Report in USA Today, More and More