Define and discuss the concept of a sampling distribution, with emphasis on the distributions of means and variances. Be sure to include the significance of sample sizes to sampling distributions.
What will be an ideal response?
Ans: A sampling distribution is a probability distribution of all possible values of a sample statistic based on samples of the same size. Every statistic has a sampling distribution. For example, there are sampling distributions for the mean, median, mode, range, variance, standard deviation, skew, kurtosis, and many other statistics. The sampling distribution of the mean (or the distribution of sample means) has a mean equal to the mean of the population being sampled no matter how large the sample is, what the population standard deviation is, or what the shape of the distribution is. The variance of the distribution of means equals the variance of the distribution being sampled divided by n.
The distribution of sample variances is like any other statistical distribution. It is simply the distribution of all possible values of the sample variance computed from samples of the same size. All sampling distributions become narrower as sample size increases.
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