Why will the sampling distribution be less variable than the

Why will the sampling distribution be less variable than the population distribution?

Solution

As sample sizes increase, the sampling distributions approach a normal distribution. With \"infinite\" numbers of successive random samples, the mean of the sampling distribution is equal to the population mean (µ).

As the sample sizes increase, the variability of each sampling distribution decreases so that they become increasingly more leptokurtic. The range of the sampling distribution is smaller than the range of the original population. The standard deviation of each sampling distribution is equal to s/root N (where N is the size of the sample drawn from the population).

Taken together, these distributions suggest that the sample mean provides a good estimate of µ and that errors in our estimates (indicated by the variability of scores in the distribution) decrease as the size of the samples we draw from the population increase.