How does the sample size affect how close to normal a distribution of either sample means or sample pro-portions will be? What are the means and standard deviations of the distributions in each case?
How does the
The larger the sample size, the more close the distribution is to that of a normal distribution. As for the spread of all sample means, theory dictates the behavior much more precisely than saying that there is less spread for larger samples. In fact, the standard deviation of all sample means is directly related to the sample size, n as indicated below.
where the standard deviation is for the samples
= population standard deviation
n =sample size
How large a sample size do we need in order to assume that sample means will be normally distributed? Well, it really depends on the population distribution, as we saw in the simulation. The general rule of thumb is that samples of size 30 or greater will have a fairly normal distribution regardless of the shape of the distribution of the variable in the population.
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