After conducting a survey, a researcher wishes to cut the standard error (and thus the marginof error) to of its original value.How will the necessary sample size change?
A)It will decrease by a factor of 3.
B)It will increase by a factor of 3.
C)It will decrease by a factor of 9.
D)It will increase by a factor of 9.
E)Not enough information is given.

Question

Quizplus · Accepted Answer

The necessary sample size will increase by a factor of 9 because the standard error of the mean is inversely proportional to the square root of the sample size. To cut the standard error to 1/3 of its original value, the square of 3 (3^2 = 9) must be applied to the sample size.

After Conducting a Survey, a Researcher Wishes to Cut the Standard