The Electronics Associates Sampling Problem

The director of personnel for Electronics Associates, Inc. (EAI), has been assigned the task of developing a profile of the company’s 2500 managers. The characteristics to be identified include the mean annual salary for the managers and the proportion of managers having completed the company’s management training program.

Using the 2500 managers as the population for this study, we can find the annual salary and the training program status for each individual by referring to the firm’s personnel records. The data set containing this information for all 2500 managers in the population is in the file named EAI.

Using the EAI data and the formulas presented in Chapter 3, we computed the popula­tion mean and the population standard deviation for the annual salary data.

The data for the training program status show that 1500 of the 2500 managers completed the training program.

Numerical characteristics of a population are called parameters. Letting p denote the proportion of the population that completed the training program, we see that p = 1500/2500 = .60. The population mean annual salary (m = $71,800), the population standard deviation of annual salary (s = $4000), and the population proportion that com­pleted the training program (p = .60) are parameters of the population of EAI managers.

Now, suppose that the necessary information on all the EAI managers was not read­ily available in the company’s database. The question we now consider is how the firm’s director of personnel can obtain estimates of the population parameters by using a sample of managers rather than all 2500 managers in the population. Suppose that a sample of 30 managers will be used. Clearly, the time and the cost of developing a profile would be substantially less for 30 managers than for the entire population. If the personnel director could be assured that a sample of 30 managers would provide adequate information about the population of 2500 managers, working with a sample would be preferable to working with the entire population. Let us explore the possibility of using a sample for the EAI study by first considering how we can identify a sample of 30 managers.

Source:  Anderson David R., Sweeney Dennis J., Williams Thomas A. (2019), Statistics for Business & Economics, Cengage Learning; 14th edition.