If you are sampling from a very large population, a doubling of the sample size will reduce the standard error of the sampling distribution by one-fourth.

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Quizplus · Accepted Answer

Doubling the sample size reduces the standard error by a factor of $\sqrt{2}$, not by one-fourth. The standard error of the mean is inversely proportional to the square root of the sample size ($n$), so increasing the sample size by a factor of 2 reduces the standard error by a factor of $\sqrt{2}$, which is approximately 1.41, not by one-fourth.

If You Are Sampling from a Very Large Population, a Doubling