The standard error of the mean decreases when:
A)the sample size decreases.
B)the standard deviation increases.
C)the standard deviation decreases or n increases.
D)the population size decreases.

Question

Quizplus · Accepted Answer

The standard error of the mean is calculated as the standard deviation of the sample divided by the square root of the sample size (SE=SD/sqrt(n)). Therefore, the standard error of the mean will decrease if the standard deviation decreases or the sample size increases. Option A is incorrect because when the sample size decreases, there is less information from which to estimate the population mean, and the standard error of the mean will increase. Option B is incorrect because the standard deviation and the standard error of the mean are two different measures; increasing the standard deviation does not necessarily affect the standard error of the mean. Option D is incorrect because the population size is not relevant for calculating the standard error of the mean.

The Standard Error of the Mean Decreases When