# Section 1.3: Simple Random Sampling

## Objectives

By the end of this lesson, you will be able to...

1. obtain a simple random sample

For a quick overview of this section, feel free to watch this short video summary:

The next section we want to discuss is how to pick a "random" sample from a population. Even more-so - what does it mean to be "random"?

## Why do we sample?

Let's suppose we want to know what ECC students think about parking on campus. It isn't possible to ask every single student, so instead we try to get a sample of students. One important characteristic that this sample must have is that it must be representative of the entire student body. (In other words, we can't have all Culinary Arts students, or all students that are fresh from high school.)

In this section and Section 1.4, we'll introduce several sampling strategies: simple random, stratified, systematic, and cluster.

## Simple Random Sampling

The first type of sampling, called simple random sampling, is the simplest. Here's the textbook definition:

A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring.

OK, so maybe that didn't sound simple. Essentially, in order to qualify as a simple random sampling process, each sample must be equally likely. You've probably already used this method without knowing it. Let's suppose you want to select a sample of 4 people from a group of 12 (see image above). Here are some common ways to select a simple random sample:

• write everyone's name on a slip of paper and draw two from a hat
• write all possible samples of size two on slips of paper and draw one from a hat
• number each individual and use technology to randomly select two integers between 1 and 30

Practically, the first two lost their effectiveness with large groups, so we'll be focusing on the latter method.

With our example of a sample size 4 from a population of 12, we might use technology to select four random integers between 1 and 12. Say we get 2, 5, 8, and 10. Our sample would then look this this: For another take, watch this YouTube video by Steve Mays.

## Random The only thing left to do, then, is to generate a random number. But how do you do that? Just pick a number from your head?

For a good explanation, watch this video from Clive Rix, at the University of Leicester in England.

OK, then how do we actually generate a random number? The "Technology" box below shows how to generate what are called "pseudo random numbers", which is a reasonable enough technique for this course.

To get a true random number, you need something more sophisticated. One solution is random.org. For information about randomness and the difference between pseudo random numbers and true random numbers, you can visit their page on an Introduction to Randomness and Random Numbers.

For the purposes of this course, feel free to use the instructions below.

## Technology

Here's a quick overview of how to generate random integers in StatCrunch.

 Select Data > Simulate Data > Uniform Enter n for Rows and 1 for Columns Enter the lower and upper limits for a and b. Press Simulate You can manually round each value, or StatCrunch can do it for you. To round, follow these steps: Select Data > Compute expression Set Y to Uniform1. Select "round(Y)" in the expression dropbox (it's the very last expression). Press Set Expression and press Compute.