Chapter 10, Problem 72CRE

Robot Cockroaches Refer to the description in exercise $10.71$. There were 22 trials with only cockroaches (no robots) that went under one shelter. In 16 of these 22 trials, the group chose the darker shelter, and in 6 of the 22 the group chose the lighter shelter. There were 28 trials with a mixture of real cockroaches and robots that all went under one shelter. In 11 of these trials, the group chose the darker shelter, and in 17 the group chose the lighter shelter. The robot cockroaches were programmed to choose the lighter shelter (as well as preferring groups; Halloy et al. 2007)

Is the introduction of robot cockroaches associated with the type of shelter when the group went under one shelter? Assume cock-roaches were randomly sampled from some meaningful population of cockroaches.

a. Use the chi-square test to see whether the presence or absence of robots is associated with whether they went under the darker or the brighter shelter. Use a significance level of $0.05$.

b. Do Fisher’s Exact Test with the data. If your software does not do Fisher’s Exact Test, search the Internet for a Fisher’s Exact Test calculator and use it. Report the $\text{p-value}$ and your conclusion.

c. Compare the $\text{p-values}$ for parts a and

b. Which do you think is the more accurate procedure? The $\text{p-values}$ that result from the two methods in this question are closer than the $\text{p-values}$ in the previous question. Why do you think that is?