Question

By how many times does the sample size have to be increased to decrease the margin of error by a factor of one fourth14​?

Answer 1

The margin of error is proportional to $\frac{1}{ \sqrt{n} }$ where n is the sample size. therefore for the M.E. to decrease by a factor of one fourth, the sample size must increase by a factor of $4^{2}=16.$.
The answer is: the sample size must increase by 16 times.

Answer 2

16 times the sample size have to be increased to decrease the margin of error by a factor of one fourth.

Step-by-step explanation:

We know that margin of error is inversely proportional to square root of sample size n,

$\rm ME\;\alpha \;\dfrac{1}{\sqrt{n} }$

So to decrease the margin of error by a factor of one fourth we have to increase the sample size by a factor of $4^2$.

16 times the sample size have to be increased to decrease the margin of error by a factor of one fourth.

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