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The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is x = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of o=4.1 inches. Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400. Which of the following statements is true? A) The margin of error for the 95% confidence interval would increase. B) The margin of error for the 95% confidence interval would decrease. C) The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed. D) The standard deviation o would decrease.

The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is x = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of o=4.1 inches. Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400. Which of the following statements is true? A) The margin of error for the 95% confidence interval would increase. B) The margin of error for the 95% confidence interval would decrease. C) The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed. D) The standard deviation o would decrease.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
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The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is x = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of o= 4.1 inches. Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400. Which of the following statements is true? A) The margin of error for the 95% confidence interval would increase. B) The margin of error for the 95% confidence interval would decrease. C) The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed. D) The standard deviation owould decrease.
Transcribed Image Text:The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured. The sample mean is x = 66.2 inches. Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of o= 4.1 inches. Suppose the heights of a simple random sample of 100 male sophomores were measured rather than 400. Which of the following statements is true? A) The margin of error for the 95% confidence interval would increase. B) The margin of error for the 95% confidence interval would decrease. C) The margin of error for the 95% confidence interval would stay the same because the level of confidence has not changed. D) The standard deviation owould decrease.
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