In this problem, we will conduct statistical analysis on the sheep experiment discussed at the beginning of the chapter. We will create variables and use OLS to analyze their relationships. Death is the dependent variable, and treatment is the independent variable. For all models, the treatment variable will equal 1 for the first 24 observations and 0 for the last 24 observations.

(a) Suppose, as in the example, that only one sheep in the treatment group died and all sheep in the control group died. Is the treatment coefficient statistically significant? What is the (two-sided) p value? What is the confidence interval?

(b) Suppose now that only one sheep in the treatment group died and only 10 sheep in the control group died. Is the treatment coefficient statistically significant? What is the (two-sided) p value? What is the confidence interval?

(c) Continue supposing that only one sheep in the treatment group died. What is the minimal number of sheep in the control group that need to die for the treatment effect to be statistically significant? (Solve by trial and error.)