Question

Explain fully how the average, standard deviation, and distribution of means of samples changes as the sample size increases.

Answer 1

Using the central limit theorem, the distribution for the sample means from any population for sample size n > 30 is given as:

Therefore the mean remains the same as the sample size increases.

The standard deviation of the sample mean decreases as the sample size increases as we can see from the above notation that the standard error of mean is inversely proportional to the square root of the sample size n.

The distribution tends to a normal distribution for a larger sample size. The normal distribution approximation is valid only for n > 30 that is the central limit theorem can only be applied to sample size n > 30