All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? ME=(z⋅s)/(sqrt(n))
Answer
A
The margin of error is multiplied by square root of 2 .
B
The margin of error is multiplied by square root of 0 point 5 .
C
The margin of error is multiplied by 0 point 5 .
D
The margin of error is multiplied by 2 .
Explanation
The margin of error is ME = (z·s)/√n. If the sample size is cut in half, the new margin of error is (z·s)/√(n/2), which is √2 times the original margin of error. Therefore, the margin of error is multiplied by the square root of 2, choice B.
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