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. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population proportion, then ________.
A) the resulting margin of error will increase and the risk of reporting an incorrect interval will increase
B) the resulting margin of error will decrease and the risk of reporting an incorrect interval will increase
C) the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
D) the resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease

Question

Quizplus · Accepted Answer

When constructing a confidence interval, increasing the confidence level (from 95% to 99% in this case) results in a wider interval due to an increased margin of error. This wider interval reflects greater certainty (or less risk) of capturing the true population parameter, thus decreasing the risk of reporting an incorrect interval.

According to a Report in USA Today, More and More