In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been:
A) 60.92 ± 2.14.
B) 50.92 ± 12.14.
C) 101.84 ± 4.28.
D) 50.92 ± 4.28.

Question

Quizplus · Accepted Answer

The width of the confidence interval is directly proportional to the standard deviation. If $\sigma$ doubles from 10 to 20, the margin of error also doubles, changing from 2.14 to 4.28. Thus, the interval becomes 50.92 ± 4.28.

In Developing an Interval Estimate for a Population Mean, the Population