Question

Random assignment Researchers recruited $20$volunteers-$8$men and $12$women-to take part in an experiment. They randomly assigned the subjects into two groups of $10$people each. To their surprise, $6$of the $8$men were randomly assigned to the same treatment. Should they be surprised? We want to design a simulation to estimate the probability that a proper random assignment would result in $6$or more of the $8$men ending up in the same group.

Get $20$identical slips of paper. Write "$M$" on $8$of the slips and "$W$" on the remaining $12$slips. Put the slips into a hat and mix well. Draw $10$of the slips without looking and place into one pile representing Group $1$. Place the other $10$slips in a pile representing Group $2$. Record the largest number of men in either of the two groups from this simulated random assignment. Repeat this process many, many times. Find the percent of trials in which $6$or more men ended up in the same group.

Short answer

The statement is valid.

Step-by-step solution

Given information

We need to find out whether it is valid or not.

Explanation

We want to simulate a random sample of size $10$with $8$of the $20$volunteers being men, and we want to figure out how likely it is that $6$or more men will be chosen.

We have $20$slips of paper with $8"M"$(men) and $12"W"$(women) on them, corresponding to $8$men and $12$women among the $20$participants.

Then, without replacing any of the slips of paper, we draw ten more. The simulation design is then legitimate, because we divide the $20$slips into two groups of ten slips each, and then we calculate the percentage of trials in which six or more men were assigned to the same group (as required).