3. In a toxicological study aiming to investigate whether there is any difference in toxicity between two doses of a new anticancer drug, 81 pairs of rats were matched according to litter, body weight, and age. Each pair of rats was randomly assigned to receive two injection doses. The results are given in Table 11.19.

Please answer the following questions:

(a) What is the design of this study?

(b) Is it appropriate to conduct a χ2 test for an independent design to test the hypothesis?

If the answer is no, why?

(c) Which method could be employed in this case? What distribution is the test based on, and what is the prerequisite for conducting the test? Please state H0 and H1 .

(d) If the sample size is insufficient, which test could be used as an alternative?

What distribution is the test based on?

(e) Test the hypothesis and interpret the result.