EXAMPLE 12 Random draws using a probability model

Suppose we consider the probabilities in Table 3 as population values. Use technology to simulate random draws using the probability model in Table 3.

Solution

Using the Step-by-Step Technology Guide on page 252, we drew samples of sizes 10, 100, 1,000, and 10,000 from the probability model in Table 3. The results are shown in Table 4.

Table 5.11: Table 4 Relative frequencies from random draws of different sizes
Employment type Rel freq

 Rel freq

 Rel freq

 Rel freq
Private company 0.60 0.62 0.566 0.596
Federal government 0.20 0.15 0.15 0.143
Self-employed 0.10 0.11 0.109 0.991
Private nonprofit 0.10 0.07 0.106 0.914
Local government 0.00 0.04 0.055 0.056
State government 0.00 0.01 0.012 0.012
Other 0.00 0.00 0.002 0.002

Note that each relative frequency tends to approach its respective probability as the sample sizes grow larger.