Question

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

Answer 1

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

Explanation:

The margin of error helps in mentioning the amount of random sampling error that occurred in a survey. Increase in the margin of error, makes the result less confidence. So the margin of error of the survey should be less.

The margin of error can be calculated in two different ways:

One is using the standard deviation of population,

Margin of error = Critical value x Standard deviation for the population

Other is using standard error of sample,

Margin of error = Critical value x Standard error of the sample