Chapter 5.1, Problem 18E

To determine

To find out whether the simulation design is valid or not.

Answer to Problem 18E

Yes, this design is valid.

Explanation of Solution

In this question, researchers recruited $20$ volunteers to take part in an experiment. And they were randomly assigned the subjects into two groups. Now, we are interested in simulating a random sample of size $10$ in which $\text{8 of the 20}$ volunteers are men and also we are interested in estimating the probability of selecting $6$ or more men.

Thus, we have $20$ slips of paper with $8$ slips containing “M” that is men and $12$ slips containing “W” that is women which corresponds with $\text{8 of the 20}$ volunteers being men. Now, next we draw $10$ slips of paper without replacement. Thus, the simulation design is then valid because we are separating the $20$ slips into two groups of $10$ slips each and then find out the percent of trials in which $6$ or more men ended up in the same group.