Chapter 5: Q. 18 (page 311)

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

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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).