Suppose that scores for men on an aptitude test have greatervariability than sco

Question

Suppose that scores for men on an aptitude test have greatervariability than scores for women on the same test. In other words,the standard deviation is greater for the population of men thanfor the population of women. Based on a sample of size 50, a 95%confidence interval for the mean score, , of all women has amargin of error of 2.2. Which of the following confidence intervalswill have a smaller 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 = 100 C. A 95% confidence interval for the mean score of men. Samplesize = 50 A) A and B B) A C) A, B, C D) C E) B Suppose that scores for men on an aptitude test have greatervariability than scores for women on the same test. In other words,the standard deviation is greater for the population of men thanfor the population of women. Based on a sample of size 50, a 95%confidence interval for the mean score, , of all women has amargin of error of 2.2. Which of the following confidence intervalswill have a smaller 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 = 100 C. A 95% confidence interval for the mean score of men. Samplesize = 50 A) A and B B) A C) A, B, C D) C E) B

Explanation / Answer

Let's look at the choices. First, a 99% confidence interval with the same setup will require alarger margin of error to capture all of the necessary data, so wecan exclude any answer choices that contain "A." For option "B," we see that there is the same confidence intervalrequired, but a larger sample size is given. Therefore, we have amore accurate estimate of the population (with the larger number ofsamples taken), so our answer choice must contain scenario "B." Finally, we consider option "C," and find that we need a largermargin of error to capture the data once more. Because the data formen has more variation, we need a larger margin to have therequired 95% confidence; therefore, we should exclude any answerchoices that contain "C." Only the second scenario, "B," will have a smaller margin of error.The correct answer is E. Hope this helps, and please rate my answer! Thanks, hp

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