Chapter 5, Problem 2SE

Simulation Suppose you are carrying out a randomized experiment to test whether loud music interferes with memorizing numbers. You have 20 college student participants. You want each participant to have a $50\%$ chance of being assigned to the experimental group (memorizes numbers while music plays) and a $50\%$ chance of being assigned to the control group (memorizes numbers with no music). Let the digits $0,1,2,3,$ and 4 represent assignment to the experimental group (music) and the digits $5,6,7,8,$ and 9 represent assignment to the control group. Begin with the first digits in the fifth line of the random number table in the back of the text.

a. Write the 20 random numbers. For each number, write M under it if it represents a student randomized to the music group and C if it represents a student randomized to the control group.

b. What percentage of the 20 participants were assigned to the music group?

c. Would it be appropriate to assign all the even numbers $\left(0,2,4,6,8\right)$ to the music group and all the odd numbers $\left(1,3,5,7,9\right)$ to the control group? Why or why not?

(In real life, researchers might sample from the random number table without replacement, to make sure that both groups have the same sample size.)