The heights of a random sample of 400 high school sophomores in a Midwestern state were measured. The sample mean, x bar = 66.2 inches. Suppose that the heights of all high school sophomore males follow a normal distribution with unknown mean, , and standard deviation, = 4.1 inches. A 95% confidence interval for . Suppose you had measured the heights of a random sample of 100 sophomore males rather than 400. Which of the following statements is true?
A) The margin of error for our 95% confidence interval would decrease.
B) I would decrease. C) The margin of error for our 95% confidence interval would increase.
D) The margin of error for our 95% confidence interval would stay the same, because the level of confidence has not changed
