Which statement is most nearly correct, other things being equal?
A)Doubling the sample size will cut the standard error of the mean in half.
B)The standard error of the mean depends on the population size.
C)Quadrupling the sample size roughly halves the standard error of the mean.
D)The standard error of the mean depends on the confidence level.

Question

Quizplus · Accepted Answer

According to the formula for standard error, as the sample size (n) increases, the standard error decreases. Quadrupling the sample size would increase it by a factor of 4, which would roughly halve the standard error of the mean. Option A is incorrect because doubling the sample size would reduce the standard error by only 1/sqrt(2) times or approximately 0.707 times. Option B is incorrect because the population size does not affect the standard error, only the sample size. Option D is incorrect because the standard error is not affected by the confidence level.

Which Statement Is Most Nearly Correct, Other Things Being Equal