Suppose that scores for men on an aptitude test have greater

Suppose that scores for men on an aptitude test have greater variability than scores for women on the same test. In other words, the population standard deviation (s) is greater for the population of men than for the population of women. Based on a sample of size 50 and a Z-interval procedure, a 95% confidence interval for the mean score, , of all women has a margin of error of 2.2. Which of the following confidence intervals will have a smaller margin of error (than 2.2)?

A.   A 99% confidence interval for the mean score of women. Sample size = 50

B.   A 95% confidence interval for the mean score of women. Sample size = 100

C.   A 95% confidence interval for the mean score of men. Sample size = 50

Solution

If we increase the sample size then margin of error decreases. Hence, with the same confidence interval, for a sample size of 100, the margin of error will be smaller than 2.2

Hence,

Option B is correct.