Explain why decreases as the size of the samples in the sampling distribution increase. Your answer should include an explanation based on the formula for and an explanation of why this formula makes sense (in other words, why would increasing the size of each sample in the sampling distribution cause to decrease?

Question

What will be an ideal response?

Answer 1

decreases when the sample size increases first because the formula for is to divide s by the square root of N. Thus, as N increases we are dividing by a larger number, resulting in a smaller number. This makes sense because as sample size increases, the mean of each of the samples should be closer to m (we are including more of the population in the samples, and thus the sample means would be more similar to m), and thus, the standard deviation (or the standard error of the mean) would be smaller because the sample means on which it is calculated would be closer to m, resulting in less variability.