After conducting a survey,a researcher wishes to cut the standard error (and thus the margin of error) to $13\frac { 1 } { 3 }$ of its original value.How will the necessary sample size change?

A) It will increase by a factor of 3.
B) It will decrease by a factor of 3.
C) It will increase by a factor of 9.
D) It will decrease by a factor of 9.
E) Not enough information is given.

Question

After conducting a survey,a researcher wishes to cut the standard error (and thus the margin of error) to

13\frac { 1 } { 3 }

of its original value.How will the necessary sample size change?

A) It will increase by a factor of 3.
B) It will decrease by a factor of 3.
C) It will increase by a factor of 9.
D) It will decrease by a factor of 9.
E) Not enough information is given.

dimetri phillips · Accepted Answer

Final Answer : C, Explanation :  To decrease the standard error (and margin of error) by a factor of  , the sample size will need to be increased by a factor of  squared (since the standard error is inversely proportional to the square root of the sample size). Therefore, the necessary sample size will increase by a factor of  x  = 121. Choice C is the correct answer.

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