Question

A confidence interval for the population mean based on 100 observations is half as wide as the same confidence interval based on 25 observations, all else being equals.

Ture or False?

Answer 1

Width of confidence interval =

where Z is test statistic at a given confidence interval and is the standard deviation.

For n = 100,

Width of confidence interval =

For n = 25,

Width of confidence interval =

Thus, the width of confidence interval for n = 25 observations is twice that for n = 100 observations.

or, the width of confidence interval for n = 100 observations is half that for n = 25 observations.

True