RESEARCH METHODOLOGY

Detailed explanation-1: -Reminder: What is a sampling distribution? The sampling distribution of a statistic is the distribution of all possible values taken by the statistic when all possible samples of a fixed size n are taken from the population.

Detailed explanation-2: -The sampling distribution of a sample mean is the distribution of all sample means for samples of a fixed size, say n, taken from some population, usually without replacement, although for mathematical convenience, sampling with replacement is investigated first.

Detailed explanation-3: -The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled. Therefore, if a population has a mean , then the mean of the sampling distribution of the mean is also . The symbol M is used to refer to the mean of the sampling distribution of the mean.

Detailed explanation-4: -As you might expect, the mean of the sampling distribution of the difference between means is: which says that the mean of the distribution of differences between sample means is equal to the difference between population means.