5. Let X1. ... Xx ~ Uniform(0, #) and let Y = max{ X1,.... X.). We want to test Ho : 0 = 1/2 versus H1 : 0 > 1/2. The Wald test is not appropriate since Y does not converge to a Normal. Suppose we decide to test this hypothesis by rejecting Ho when Y > c. (a) Find the power function. (b) What choice of c will make the size of the test .05? (c) In a sample of size n = 20 with Y=0.48 what is the p-value? What conclusion about Ho would you make? (d) In a sample of size n = 20 with Y=0.52 what is the p-value? What conclusion about Ho would you make? 6. There is a theory that people can postpone their death until after an important event. To test the theory, Phillips and King (1988) collected data on deaths around the Jewish holiday Passover. Of 1919 deaths, 922 died the week before the holiday and 997 died the week after. Think of this as a binomial and test the null hypothesis that e = 1/2. Report and interpret the p-value. Also construct a confidence interval for e. 7. In 1861, 10 essays appeared in the New Orleans Daily Crescent. They were signed "Quintus Curtius Snodgrass" and some people suspected they were actually written by Mark Twain. To investigate this, we will consider the proportion of three letter words found in an author's work. From eight Twain essays we have: 225 .262 .217 .240 .230 .229 .235 .217 From 10 Snodgrass essays we have: .209 .205 .196 .210 .202 .207 .224 .223 .220 .201 (a) Perform a Wald test for equality of the means. Use the nonparamet- ric plug-in estimator. Report the p-value and a 95 per cent confidence interval for the difference of means. What do you conclude? (b) Now use a permutation test to avoid the use of large sample methods