In developing an interval estimate for a population mean,the population standard deviation $\sigma$ was assumed to be 8.The interval estimate was 50.0 $\pm$ 2.50.Had $\sigma$ equaled 16,the interval estimate would be 100 $\pm$5.0.

Question

Quizplus · Accepted Answer

The interval estimate is affected by the standard deviation, but doubling the standard deviation does not double the interval estimate. The interval width is proportional to the standard deviation, so if the standard deviation doubles, the interval width would also double, but the center of the interval (the mean) remains the same.

In Developing an Interval Estimate for a Population Mean,the Population σ\sigmaσ

In Developing an Interval Estimate for a Population Mean,the Population $\sigma$