Refer to previous exercise. Suppose you wanted a large enough sample to estimate the probability of preferring the new drug to within 0.05, with confidence 0.95. If the true probability is 0.80, about how large a sample is needed?

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Previous exercise: In a crossover trail comparing a new drug to a standard,??denotes the probability that the new one is judged better. It is desired to estimate??and test??against??. In 20 independent observations, the new drug is better each time.

(a) Find and sketch the likelihood function

(b) Give the ML estimate of??. Conduct a wald test and construct a 95% score confidence interval.

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T T Ho: π = 0.5 На : п + 0.5 T T T Ho: π = 0.5 На : п + 0.5 T