Question

when collecting a random sample from a normally distributed population what impact will increasing the sample size have on the distribution of the sample in other words if you took samples of 10, 50,100 and 300 how would you expect the distribution of the four samples to differ

Answer 1

The population mean of the distribution of sample means is the same as the population mean of the distribution being sampled from. Thus the mean of the distribution of the means never changes. The standard deviation of the sample means, however, is the population standard deviation from the original distribution divided by the square root of the sample size. Thus as the sample size increases, the standard deviation of the means decreases; and as the sample size decreases, the standard deviation of the sample means increases.