The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured.The sample mean is  = 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  would decrease. class=answers-bank-image d-inline rel=preload = 66.2 inches.Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of  = 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  would decrease.

Question

The heights of a simple random sample of 400 male high school sophomores in a Midwestern state are measured.The sample mean is    = 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    would decrease. class=answers-bank-image d-inline rel=preload > = 66.2 inches.Suppose that the heights of male high school sophomores follow a Normal distribution with a standard deviation of    = 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    would decrease.

Jessica Vargas · Accepted Answer

Final Answer : A, Explanation :  The margin of error for a confidence interval is directly proportional to the sample size. As the sample size decreases from 400 to 100, the margin of error will increase. Therefore, choice A is correct. The level of confidence does not affect the margin of error in this case, so choice C is incorrect. The standard deviation is not affected by the sample size, so choice D is also incorrect.

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