5. In the toxicological study of a new anticancer drug, 78 rats were randomly divided into two groups of 39. One group received a low-dose injection and the other a high-dose injection of the drug. Eighteen rats in the high-dose group and nine rats in the low-dose group died.

(a) What is the design of this study?

(b) Which type of statistical test could be used to deal with this type of data, and what theorem should hold when applying the test method?

(c) Conduct hypothesis testing to determine whether there is a difference in population rates of death between the two groups.

(d) Compute and interpret the 95% CI for the difference in population rates of death between the two groups.

(e) Using a one-sided test at a significance level of  =0.05, what is the power of this test?

(f) How large a sample size is needed if an equal sample size is assigned in each group, for a one-sided and two-sided test, respectively, with a significance level of 0.05 and a power of 80%. Is the sample size requirement higher in the one-sided test or the two-sided test, explain your answer?