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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.

Step by step solution

01

Given information

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

02

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).

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