Question

A 95% confidence interval estimate for a population mean u is determined to be 75.38 to 86.52. If the confidence level is reduced to 90%, the confidence interval for u A. becomes wider B. remains the same C. becomes narrower D.. none of the above answers is correct

Answer 1

Answer: the correct option is C

Explanation:

The 95% confidence interval for the population mean is determined to be 75.38 to 86.52. If the confidence interval is reduced to 90%, the the confidence interval for u will become narrower. This is because there is a reduction in the margin of error. It would result to lesser possible values for the mean.

Answer 2

C. becomes narrower

Explanation:

If the confidence level is reduced from 95% to 90%, then, the confidence interval for u becomes narrower, i.e., we are less sure that the true value of u is contained inside the new interval. With a 95% confidence interval there is a probability of 0.95 that the parameter u is inside the interval and with a 90% confidence interval there is a probability of 0.90 that the parameter u is inside the interval.