Recall Example 4.3 from the text. The goal is to determine if the average number of girls in three-child families is 1.5, the theoretical value. We will confirm this result using the five-step method.
In the text, we flip a coin three times and count the number of heads. The number of heads stands for the number of girls in the family, which assumes that boys and girls are equally likely. Define the box model (Step 1) in a new five-step simulation. In the Value column, enter a 0 (for a boy) and a 1 (for a girl) each with the default count of 1. No other values should be specified. Click on the Next button to go to Step 2.
A trial is three flips or equivalently three draws with replacement from the box model. From the Define the sample: menu, select Draw n With Replacement. In the resulting n= field, enter 3 because this is the number of draws for each trial. Click on the Next button to go to Step 3.
This time we just want to count how many of the children are girls, i.e., how many of the flips are heads or how many of the draws are 1 values. Since we have defined boys to be 0 and girls to be 1, we just need to sum the draw values to count the number of girls. Therefore, select Sum from the Statistic of interest (X) menu. Click on the Next button to go to Step 4.
Press the 1 button. You will see three numbers in the Current Simulation field, each with a value of 0 or 1. For example, you might get 1 1 0 representing a girl, a girl, and a boy. The number of 1 values, or the sum of the draws, will appear in the Sum field. In this case the sum is 2, i.e., this specific simulated family had 2 girls. Click the 100 button to create 100 more simulated families. Click on the Next button to go to Step 5.
In the Mean field, you see the average number of 1 values per trial, which represents the average number of girls per three-child family. Is the average close to 1.5? Go back to Step 4 and increase the number of trials by 2000 (by clicking on the 1000 button twice). Should the average get closer to 1.5? Characterize the shape of the frequency histogram which only takes on values of 0, 1, 2, and 3. Why? Do you believe the probability of getting 1 girl (2 boys) is equal to that of getting 1 boy (2 girls)? Why?