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5, (15 points) In a clinical trial comparing a new drugto a standard drug, let π denote the probability that the new drug is better. Consider estimating r and testing Ho T 5 In 5 20 independent observations, the new drug is better just one time. (a) Find the maximum likelihood estimate of π. (b) Conduct a Wald test and construct a 95% Wald confidence interval for T. Interpret the (c) Conduct a score test and construct a 95% score confidence interval for π. Interpret the re- (d) Conduct a likelihood ratio test and construct a 95% likelihood-based confidence interval result. sult. Hint: For the CI you can use equation 1.14 in the book or numerically/computationally solve. If you numerically solve then turn in your R code. for π. Interpret the result. Hint: Solve for the CI numerically/computationally. Turn in your R code. (e) Construct an exact binomial test. Hint: See Section 1.4.4 of the tertbook. Note that the eract test involves calculating the probability of observing more extreme events based on the null binomial distribution. (f) Comment on how the results from the different tests and confidence intervals compare.
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OLCT) 20 TCI-maximized at T0o2 0.5 t 1.96 (9.35 20 0.2808, o,귀91 Noou testing the hypheu for Π: 2O ,4722. Null hypothests (C) likelihood Confidence fnheaal, 95 % 乙二R介 TCI-TT eC-o) 20 Can Sede nce inte nal chould be Co, betuen o and

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