Find a simple random sample of five clients for the problem presented in Example 2.

Approach  The approach is similar to that given in Example 2.

Step 1 Obtain the frame and assign the clients numbers from 01 to 30.

Step 2 Randomly select five numbers using a random number generator. To do this, we must first set the seed. The seed is an initial point for the generator to start creating random numbers—like selecting the initial point in the table of random numbers. The seed can be any nonzero number. Statistical software such as StatCrunch, Minitab, or Excel can be used to generate random numbers, but we will use a TI-84 Plus C graphing calculator. The steps for obtaining random numbers using StatCrunch, Minitab, Excel, and the TI-83/84 Plus/84 Plus C graphing calculator can be found in the Technology Step-by-Step.

Data from Example 2

The accounting firm of Senese and Associates has grown. To make sure their clients are still satisfied with the services they are receiving, the company decides to send a survey out to a simple random sample of 5 of its 30 clients.

Approach

Step 1 The clients must be listed (the frame) and numbered from 01 to 30.

Step 2 Five unique numbers will be randomly selected. The clients corresponding to the numbers are sent a survey. This process is called sampling without replacement.

In a sample without replacement, an individual who is selected is removed from the population and cannot be chosen again. In a sample with replacement, a selected individual is placed back into the population and could be chosen a second time. We use sampling without replacement so that we don’t select the same client twice.