Consider a normally distribution population with known variance.A 95% confidence interval is computed based on sample of 25 observations.If we take a new sample of 100 observations and compute a second 95% confidence interval based on the new sample,we know that the width of the second confidence interval will be exactly ____ times the width of the first confidence interval.
A)2
B)0.5
C)4
D)0.25
E)We cannot answer this question without knowing the sample means from both samples.

Question

Quizplus · Accepted Answer

The width of a confidence interval depends on the sample size and the confidence level, but not on the population variance. Since the sample size is increasing from 25 to 100, the second confidence interval will have a smaller width, but the confidence level remains the same. A 95% confidence interval for a sample of 25 observations has a width of 2 times the standard error of the mean. Therefore, a 95% confidence interval for a sample of 100 observations will have a width that is 1/2 times the width of the first confidence interval, or 0.5 times.

Consider a Normally Distribution Population with Known Variance