Let X1, ., Xn - Uniform(0, 0) and let Y = max{X1, ., Xn). We want...

 

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Let X1, ., Xn - Uniform(0, 0) and let Y = max{X1, ., Xn). 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 cwill 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? Let X1, ., Xn - Uniform(0, 0) and let Y = max{X1, ., Xn). 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 cwill 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?

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