In Exploration 4.2 you used the Randomizing Subjects applet to randomly assign subjects to two groups. At the end of the exploration, you blocked on a person’s sex and saw this eliminate the variability in the difference in proportion of males. You should have also seen that blocking on a person’s sex reduced the variability in the difference in height. This reduction in variation happened because sex is associated with height. What about other variables? Open up the Randomizing Subjects applet to answer (a) and (b). 

a. Another variable that can be used in the applet is “balance gene,” which is categorical. Let’s see if we get the same benefits of reduced variability with this variable, like we did with height, when blocking on sex. Select the Reveal gene? option, use the pull-down menu to display the distribution of the difference in the proportion of subjects with the balance gene in the two groups, and then do at least 1,000 replications of random assignment. Select the Both option to see the two distributions and summary statistics of difference in the proportion of subjects that have the gene. The one labeled CR is completely randomized, and the one labeled RAB is randomized block. What are the standard deviations of the graph of the differences in the proportions of balance genes in each treatment for the randomized block design and for the completely randomized design? How do the standard deviations compare? Does it appear that a person’s sex is associated with the balance gene? 

b. Repeat part (a) of this question, except look at the quantitative variable called factor x.