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? Design and carry out a simulation to estimate the probability that the random assignment puts $6$or more men in the same group. Follow the four-step

process.

Short answer

There will be $2$ to $6$ men as a result. Yes, they should be taken aback.

Step-by-step solution

Step 1. Given Information    

There were a total of volunteers $n=20,M=8,W=12$ We'll need to devise and carry out an experiment to determine the likelihood that the random selection will result in a group of six or more males.

Step 2. Concept Used  

We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between $0$(never happens) and $1$(happens frequently) (always occurs).

Step 3. Explanation

We should, in order to carry out the simulation, Use two-digit numbers instead of three-digit numbers. Assign the numbers to $01$to $08$a man. A woman is represented by the numerals $09$to $20$ through Ignore the numerals 00 through , as well as the number $21$to $99$Pick ten numbers at random between $01$and $20$, with no repetitions permitted. Count how many men are in the sample. Rep this simulation as many times as you like. You'll probably get between $2$and $6$males as a result, and sure, they should be startled.