Chapter 5.1, Problem 17E

To determine

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

Answer to Problem 17E

No, this design is not valid.

Explanation of Solution

In this question the teacher Mr Millar collects students’ notebooks and checks their homework. And he randomly selects four assignments to inspect for all the students. Now, we are interested in simulating a random sample of size $4$ in which two thirds of the assignment are completed and we are interested in estimating the probability of selecting $1$ or fewer completed assignments. Thus, $30$ slips of paper with $10$ slips containing “N” that is not completed and $20$ slips containing “C” that is completed, which corresponds with two-thirds of the assignment being complete. Thus, we draw $4$ slips of paper with replacement. The simulation design is then not valid because it is possible to select the same assignment on each trial which is not possible when Mr Millar selects $4$ of your homework assignments. Thus, to make the simulation design valid, the slips should have been drawn without replacement.