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 ± 2.50. Had $\sigma$ equalled 16, the interval estimate would have been 100 ± 5.0.

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Quizplus · Accepted Answer

The interval estimate depends on the standard deviation, but doubling the standard deviation does not directly double the interval estimate's center (mean) or necessarily result in a doubling of the margin of error in a straightforward manner as implied. The calculation of an interval estimate involves the standard deviation, but the center of the interval (mean) is determined by the sample data, and the margin of error is affected by both the standard deviation and the sample size, not just the standard deviation alone.

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