4.3 Notes/Examples

4.3 Summary Notes

Random Selection

We have discussed that it is important to choose samples randomly in order to reduce bias, but we haven't discussed how to actually carry out the process. There are many ways to make random selections. A common way to choose things at random is to use a 'big hat', or box, or bowl, etc. For example, suppose that a teacher wanted to randomly select 5 students every day, from a class of 34 students, to hand in their homework to be graded. Each day she has all of the students' names in a big fish bowl. She will mix the names up and select 5 names. These students will turn their homework papers in right then, and the other students will not need to. The five selected names will be put back in the fishbowl, so they may be selected again tomorrow. This is an example of an SRS of size 5 of her class. Every student has an equal probability (5/34 or 14.7% chance) of being required to turn in his or her homework on any given day and any combination of five students may be chosen. One student may end up turning in her assignment several days in a row, while another student may never need to turn hers in all year long. The idea of a 'big hat' is a good method for random selection when working with small populations, but it is not always practical.

Random selections can be made by flipping coins, rolling dice, or spinning a spinner. These days, most random selections can be done using technology such as a computer program or a random number generator on a graphing calculator, Another way that random selections are made in statistics is by using a random digit table. A random digit table is a long list of randomly generated digits from 0 to 9. The digits are listed in groups of five simply to make it easier to read and not lose your place. Imagine that someone has a ten-sided die with each digit from 0 to 9 marked on a side. They sit down, roll the die and write down the digit that appears, then they roll it again and write down the digit that appears, then they do this again and again. As you can imagine, this would take quite a while, but would result in a long list of random digits. This is basically what a random digit table is. There is a random digit table in the appendix for you to use.

How to Use a Table of Random Digits

There is a process to follow when using a random digit table to make your selection. You need to report your process with enough detail that if someone else were to follow your steps, they would end up with the exact same randomly selected numbers. The purpose of this is to prove, if needed, that your selection process was truly random so that no one can accuse you otherwise. The following example illustrates the steps you will need to follow (and explain) when using a random digit table to make your random selection. The random digit table can be found in the appendix.

Example 1

Five boxes, each containing 24 cartons of strawberries, are delivered in a shipment to a grocery store. The produce manager always selects a few cartons randomly to inspect. He knows better than to just look at some of the cartons on the top or only in one box, because sometimes the rotten ones are on the bottom. Today he wishes to select a total of 6 cartons to inspect. He has the boxes arranged in order and has a set way to count the cartons inside each box. Explain the process used to make the random selection using a random digit table.

Example 2

Five of the employees at the Stellar Boutique are going to be selected to go to a training in Las Vegas for four days. Everyone wants to go of course, so the owner has decided to make the selection randomly. She has decided to send two managers and three sales representatives. The employees' names are listed in the table below.

a) What type of sampling method is this?

b) Explain the process she can follow to use a random digit table, starting at line #108, to select the employees who will get to go to the training. Select the managers first, then select the sales representatives.

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