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Teach yourself statistics

# Simple Random Sampling

Simple random sampling refers to a sampling method that has the following properties.

• The population consists of N objects.
• The sample consists of n objects.
• All possible samples of n objects are equally likely to occur.

An important benefit of simple random sampling is that it allows researchers to use statistical methods to analyze sample results. For example, given a simple random sample, researchers can use statistical methods to define a confidence interval around a sample mean. Statistical analysis is not appropriate when non-random sampling methods are used.

## Sample Selection

There are many ways to select a simple random sample. One way would be the lottery method. Each of the N population members is assigned a unique number. The numbers are placed in a bowl and thoroughly mixed. Then, a blind-folded researcher selects n numbers. Population members having the selected numbers are included in the sample.

## Random Number Generator

In practice, the lottery method described above can be cumbersome, particularly with large sample sizes. As an alternative, use Stat Trek's Random Number Generator. With the Random Number Generator, you can select up to 10,000 random numbers quickly and easily. The Random Number Generator can found in the Stat Trek main menu under the Stat Tools tab. Or you can tap the button below.

Problem 1

The principal of Thomas Jefferson Elementary School wants to assess reading achievement of third graders. He asks the vice principal to put together a list of all the third graders. Then, the principal randomly selects a student from the first three students on the list. Starting with that student, the principal selects every third student for the assessment. For example, if student number 2 were the first student selected, the sample would consist of students number 2, 5, 8, 11, 14, etc.

Is this an example of simple random sampling?

(A) Yes
(B) No
(C) Not enough information to say for sure.

Solution

The correct answer is (B). This is not an example of simple random selection, because each possible sample is not equally likely to occur. For example, if student number 2 were in the sample, the sample could never include students number 1 or 3. The selection method described in this problem is an example of a systematic random sample, not a simple random sample.