Sampling Methods

The Summary from class is outlined below.  It outlines our textbook, " Lind. (2005). Statistical techniques in business & economics (11th ed). New York: McGraw-Hill, Chapter 8."

What is a Sample?

"A probability sample is a sample selected such that each item or person in the population being studied has a known likelihood of being included in the sample."

Types of Sampling

1. Simple Random Sample: A sample formulated so that each item or person in the population has the same chance of being included.

2. Systematic Random Sampling: The items or individuals of the population are arranged in some order. A random starting point is selected and then every kth member of the population is selected for the sample. 1-in-L samples. A sample taken by moving systematically through the population. One might randomly select one the first 200 population units and then systematically sample every 200th population unit thereafter.

3. Stratified Random Sampling: A population is first divided into subgroups, called strata, and a sample is selected from each stratum. Simple random samples from non-overlapping subpopulations or strata. Could be (1) Partitioned (Divided) Population, (2) Non-overlapping subpopulations, or (3) (Strata) Difference between groups to compare differences

4. Cluster Sampling: A population is first divided into primary units then samples are selected from the primary units. Random samples of “clusters” of units.  Could be (1) Random samples of “clusters” of units or (2) Very large populations

5. In nonprobability samples, inclusion in the sample is based on the judgment of the person selecting the sample.

Why Sample?  Sample if:

1. It is physical impossible to check all items in the population.

2. The cost of studying all the items in a population is too high.

3. The sample results are usually adequate. 

4. Contacting the whole population is too time-consuming.

5. The destructive nature of certain tests profits testing all element in the population.

The sampling error is the difference between a sample statistic and its corresponding population parameter.

The sampling distribution of the sample mean is a probability distribution consisting of all possible sample means of a given sample size selected from a population.

Central Limit Theorem:

For a population with a mean : and a variance F2 the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed.

The mean of the sampling distribution equal to : and the variance equal to F2/n.

Point Estimates:

 Are one value ( a single point) that is used to estimate a population parameter. Such as:

1. sample mean,

2. the sample standard deviation,

3. the sample variance,

4. the sample proportion.

If a population follows the normal distribution, the sampling distribution of the sample mean will also follow the normal distribution. To determine the probability a sample mean falls within a particular region, use:

If the population does not follow the normal distribution, but the sample is of at least 30 observations, the sample means will follow the normal distribution. To determine the probability a sample mean falls within a particular region, use:

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