In a crossover trial comparing a new drug to a standard, 7 denotes the probability that the new one is judged better. It is desired to estimate T and test Ho : 7 = 0.5 against Ha : 7 # 0.5. In 20 independent observations, the new drug is better each time. a. Find and sketch the likelihood function. Give the maximum likelihood estimate of T. b. Conduct a Wald test and construct a 95% Wald confidence interval for T. c. Conduct a score test, reporting the P-value. Construct a 95% score confidence interval. d. Conduct a likelihood-ratio test and construct a likelihood-based 95% confidence in- terval. e. Suppose that researchers wanted a sufficiently large sample to estimate the probabil- ity of preferring the new drug to within 0.05, at confidence level 95%. If the true probability is 0.90, how large the sample size should be