For a given confidence level and population standard deviation σ,the width of the confidence interval for the population mean is wider,the smaller the sample size n.

Question

For a given confidence level  and population standard deviation σ,the width of the confidence interval for the population mean is wider,the smaller the sample size n.

Quizplus · Accepted Answer

This is true because as the sample size decreases, there is more uncertainty in the estimate of the population mean and therefore a wider confidence interval is needed to account for this uncertainty. Conversely, as the sample size increases, the estimate of the population mean becomes more accurate and a narrower confidence interval can be used.

For a Given Confidence Level and Population Standard Deviation