Question

Brian asked Leslie: "What is a sampling distribution?” and Leslie said:

“This is the sample of samples or the mean of the means. You obtain a sample from the population, compute the mean or proportion, put the sample back and repeat the same procedure many times. Afterwards, you get a distribution of many samples and that is the sampling distribution. You also get the mean of many sample means.”

• Is she right?
• Why or why not?

The sampling distribution is said to be a bridge between the sample and the population.

• What do you think this means? (When formulating your response, please differentiate between sample statistics and parameters)

Answer 1

Leslie defined the sampling distribution perfectly. I mean she was right. Because as we define the sampling distribution is- a graph of statistics for your sample data. What we actually do in this process is that- we draw a samples from population and find a pattern of getting samples from the concerned population which gives a distribution of getting samples information (or sample statistics). This process of getting sample statistics is defined as sampling distribution. Because we know that a sampling distribution is a distribution of the sample statistics. In statistics, sampling distribution or finite-sampling distribution is the probability distribution of a given random-sample based statistic.

A statement- the sampling distribution is said to be a bridge between the sample and the population, is flawlessly said. Let's illustrate it with an example-

Let us consider that we have given a population having parameters and and these parameters have not defined i.e. unknown. To find an estimate of population constants (parameters) we draw samples from the concerned population and using the sample information (i.e. sample statistics) we find out an estimate of population constants (parameters) and using sample means and sample variances (we can also say it sample statistics i.e. , ) we get an estimate of population constants ( , ). Hence, we can say that sampling distribution is known as bridge between sample and population.

Sample statistics- sample constants are generally known as sample statistics. Ex.- , , etc.

Parameters- population constants are defined as parameters. Ex.- , , etc.