Question

23. What is the effect of choosing a larger sample size for the sampling distribution? a mean increases, standard deviation unchanged b) mean decreases, standard c) mean unchanged, standard deviation increases d) mean unchanged, standard deviation decreases e) no effect

Answer 1

Answer

We know that the sample mean is a consistent estimator of population mean, i.e. it is independent of the sample size. So there is no effect of sample size on the sample mean.

So, we can say that the mean remains same or unchanged.

Standard deviation is given as $\sigma/\sqrt{n}$

This shows that when n increases, standard deviation decreases and when n decreases, standard deviation increases.

So, when choosing a larger sample size for the sampling distribtution, it will definitely decrease or reduce the standard deviation.

We can say that mean remains same or unchanged with larger sample size and standard deviation decrease with choosing a larger sample size

So, option D is correct answer