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 is greater for the population of
Men than for the population of women. Based on a sample of size 50, a 95% confidence interval for
The mean score, $\mu ,$ , of all women has a margin of error of 2.2. Which of the following confidence
Intervals will have a smaller margin of error?
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
A)C
B)B
C)A
D)A, B, C

Question

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 is greater for the population of
Men than for the population of women. Based on a sample of size 50, a 95% confidence interval for
The mean score, $\mu ,$ , of all women has a margin of error of 2.2. Which of the following confidence
Intervals will have a smaller margin of error?
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 
A)C
B)B
C)A
D)A, B, C

Quizplus · Accepted Answer

The margin of error in a confidence interval depends on the critical value (which is determined by the confidence level), the standard deviation of the population, and the sample size. A higher confidence level (like 99% compared to 95%) increases the critical value, thus increasing the margin of error, so option A will not have a smaller margin of error. Increasing the sample size decreases the margin of error because it decreases the standard error of the mean, so option B will have a smaller margin of error. Option C involves men, who have a greater variability than women, which would generally lead to a larger margin of error, not a smaller one, when all other factors are equal. Therefore, only option B is correct.

Suppose That Scores for Men on an Aptitude Test Have μ,\mu ,μ,

Suppose That Scores for Men on an Aptitude Test Have $\mu ,$