A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been ________ and the probability of making an error would have been ________.
A) wider; smaller
B) narrower; smaller
C) wider; unchanged
D) narrower; unchanged

Question

Quizplus · Accepted Answer

If a bigger sample had been used instead, then the 95% confidence interval would have been narrower because as the sample size increases, the sample mean becomes a better estimator of the population mean, resulting in a smaller standard error. However, the probability of making an error would have been unchanged because the level of confidence remains the same.

A Sample of a Given Size Is Used to Construct