Question

In a crossover trial comparing a new drug to a standard, π denotes the probability that the new one is judged better. It is desired to estimate π and test H0 : π = 0.5 against H1 : π =/= 0.5. In 20 independent observations, the new drug is better each time.

(a) Find and PLOT the likelihood function, but I know it's. Give the ML estimate of π.

(d) Suppose that researchers wanted a sufficiently large sample to estimate the probability of preferring the new drug to within 0.05, with confidence 0.95 (i.e., the 95% confidence interval is of length 0.1), If the true probability is 0.80, about how large a sample is needed based on Wald type confidence interval?

Answer 1

d)

length of confidence interval = 2 * 1.96 * sqrt(p(1-p)/n) < 0.1

here p= 0.8, hence

2 * 1.96 * sqrt(p(1-p)/n) < 0.1

2*1.96*sqrt(0.8*0.2/n) < 0.1

sqrt(n) > 15.68

n > 245.86

= 246