Suppose you want to decrease your margin of error by a factor of 3. by what factor, do you need to increase your sample size? in other words, if you want to decrease your margin of error from 12% to 4% by what factor do you need to increase your sample size?

The sample size, n required to produce a margin of error, M, in a probability proportion distribution is given by:



The above formular shows that the sample size is inversely proportional to the Margin of error.

Then we have:



where k is some constant.

Now suppose we decrease M by a factor of 3,





Therefore, if we decrease the Margin of error by a factor of 3, we need to increase the sample size by a factor of 9.