EXAMPLE 4 How to choose an SRS using a table of random digits

To repeat Example 3, we begin by assigning numerical labels to the 30 clients.

Step 1: Label. Give each client a numerical label, using as few digits as possible. Two digits are needed to label 30 clients, so we use labels

01, 02, 03, . . . , 28, 29, 30

It is also correct to use labels 00 to 29 or even another choice of 30 two-digit labels. Here is the list of clients, with labels attached, using 01 to 30:

01 A-1 Plumbing 16 JL Appliances
02 Accent Printing 17 Johnson Commodities
03 Action Sport Shop 18 Keiser Construction
04 Anderson Construction 19 Liu’s Chinese Restaurant
05 Bailey Trucking 20 MagicTan
06 Balloons Inc. 21 Peerless Machine
07 Bennett Hardware 22 Photo Arts
08 Best’s Camera Shop 23 River City Antiques
09 Blue Print Specialties 24 Riverside Tavern
10 Central Tree Service 25 Rustic Boutique
11 Classic Flowers 26 Satellite Services
12 Computer Answers 27 Scotch Wash
13 Darlene’s Dolls 28 Sewer’s Center
14 Fleisch Realty 29 Tire Specialties
15 Hernandez Electronics 30 Von’s Video Games

29

Step 2: Table. Enter Table A anywhere and read two-digit groups. Suppose we enter at line 130, which is

69051 64817 87174 09517 84534 06489 87201 97245

The first 10 two-digit groups in this line are

69 05 16 48 17 87 17 40 95 17

Each two-digit group in Table A is equally likely to be any of the 100 possible groups, 00, 01, 02, . . . , 99. So two-digit groups choose two-digit labels at random. That’s just what we want.

Joan used only labels 01 to 30, so we ignore all other two-digit groups. The first five labels between 01 and 30 that we encounter in the table choose our sample. Of the first 10 labels in line 130, we ignore five because they are too high (over 30). The others are 05, 16, 17, 17, and 17. The clients labeled 05, 16, and 17 go into the sample. Ignore the second and third 17s because that client is already in the sample. Now run your finger across line 130 (and continue to line 131 if needed) until five clients are chosen.

The sample is the clients labeled 05, 16, 17, 20, 19. These are Bailey Trucking, JL Appliances, Johnson Commodities, MagicTan, and Liu’s Chinese Restaurant.