Chapter 10, Problem 71CRE

Robot Cockroaches Cockroaches tend to rest in groups and prefer dark areas. In a study by Halloy et al. published in Science Magazine in November 2007, cockroaches were introduced to a brightly lit, enclosed area with two different available shelters, one darker than the other. Each time a group of cockroaches was put into the brightly lit area will be called a trial. When groups of 16 real cockroaches were put in a brightly lit area, in 22 out of 30 trials, all the cockroaches went under the same shelter. In the other 8 trials, some of the cock-roaches went under one shelter, and some under the other one.

Another group consisted of a mixture of real cockroaches and robot cockroaches (4 robots and 12 real cockroaches). The robots did not look like cockroaches but had the odor of male cockroaches, and they were programmed to prefer groups (and brighter shelters). There were 30 trials. In 28 of the trials, all the cockroaches and robots rested under the same shelter, and in 2 of the trials they split up.

Is the inclusion of robots associated with whether they all went under the same shelter? To answer the following questions, assume the cockroaches are a random sample of all cockroaches.

a. Use a chi-square test for homogeneity with a significance level of $0.05$ to see whether the presence of robots is associated with whether roaches went into one shelter or two.

b. Repeat the question using Fisher’s Exact Test. (If your software will not perform the test for you, search for Fisher’s Exact Test on the Internet to do the calculations.) Conduct a two-sided hypothesis test so that the test is consistent with the test in part a.

c. Compare the $\text{p-values}$ and conclusions from part a and part

b. Which statistical test do you think is the better procedure in this case? Why?