The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, 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

The margin of error increases with a higher confidence level (99% vs. 95%) because a wider interval is needed to be more confident that it contains the population mean. The risk of reporting an incorrect interval decreases because a 99% confidence interval is more likely to contain the population mean than a 95% confidence interval.

The Ages of MBA Students at a University Are Normally