Low doses of the insecticide toxaphene may cause weight gain in rats (Chu et al., XXXXXXXXXXA sample of 20 rats are given toxaphene in their diet, while a control group of 8 rats are not given...

Low doses of the insecticide toxaphene may cause weight gain in rats (Chu et al., 1988). A sample of 20 rats are given toxaphene in their diet, while a control group of 8 rats are not given toxaphene. Assume further that weight gain among the treated rats is normally distributed with a mean of 60 g and a standard deviation of 30 g, while weight gain among the control rats is normally distributed with a mean of 10 g and a standard deviation of 50 g. Using simulation, compare confidence intervals for the difference in mean weight gain, using the pooled variance estimate and the Welch approximation. Which type of interval is correct more often?

Repeat the simulation experiment under the assumption that the standard deviations are 40 g for both samples. Is there a difference between the two types of interval now? Hint: Is one of the methods giving systematically larger confidence intervals? Which type of interval do you think is best?