Sampling Distribution of Sample Statistics

Abstract

We stated in Chapter 9 that the process of statistical inference (whether estimation or hypothesis testing) depends on knowledge of what is referred to as the sampling distribution of sample statistics. To illustrate the idea of a sampling distribution, consider the example of the distribution of the variable X, which measures the expenditure by customers in a supermarket, so that X _i measures the expenditure of the ith customer. Suppose we are interested in the mean expenditure, µ, of all customers, and intend to guess or estimate its value by taking a random sample of 100 customers, recording the expenditure of each customer in the sample, and calculating the mean expenditure of this sample, which we denote $$₁ (we have added the subscript 1 because this is the first of a number of samples we will consider). $$₁, is calculated using equation (4.4) i.e. $$₁ = ΣX _i /n, where the X _i are the sample values and n is the sample size. $$₁ will be a random variable because its value will not be known until an experiment is performed, the ‘experiment’ in this case consists of determining how much each customer spends.