Question

Notebook check Every $9$weeks, Mr. Millar collects students' notebooks and checks their homework. He randomly selects $4$different assignments to inspect for all of the students. Marino is one of the students in Mr. Millar's class. Marino completed $20$homework assignments and did not complete $10$assignments. He is surprised when Mr. Millar only selects $1$assignment that he completed. Should he be surprised? To find out, we want to design a simulation to estimate the probability that Mr. Millar will randomly select $1$or fewer of the homework assignments that Marino completed.

Get $30$identical slips of paper. Write "$N$" on 10 of the slips and "$C$" on the remaining $20$slips. Put the slips into a hat and mix well. Draw $1$slip without looking to represent the first randomly selected homework assignment, and record whether Marino completed it. Put the slip back into the hat, mix again, and draw another slip representing the second randomly selected assignment. Record whether Marino completed this assignment. Repeat this process two more times for the third and fourth randomly selected homework assignments. Record the number out of the $4$randomly selected homework assignments that Marino completed in this trial of the simulation. Perform many trials. Find the proportion of trials in which Mr. Millar randomly selects $1$or fewer of the homework assignments that Marino completed.

Short answer

It is not valid as the slips of paper should be drawn without any replacement.

Step-by-step solution

Given information

We need to find whether it is valid or not by giving the reason.

Explanation

We're interested in replicating a four-person random sample with two-thirds of the assignments completed (as $20$of the $30$tasks were finished) and assessing the likelihood of selecting one or fewer completed assignments.

The $30$slips of paper, $10$with "$N$" (not complete) and $20$with "$C$" (complete), correspond to two-thirds of the assignments done (as $20$of the $30$assignments are completed).

We then draw four replacement slips of paper. When Mr. Millar chooses four of your homework assignments, the simulation design is invalid since it is feasible to select the same assignment on each trial, which is not conceivable when Mr. Millar chooses four of your homework assignments. The slips should have been drawn without replacement in order for the simulation design to be legitimate.