Question
1.Suppose {Y 1 , . . . , Y n } are IID from Uniform(0, ) Let T = / , where = max( Y
1.Suppose {Y1, . . . , Yn} are IID from Uniform(0,) Let T = /, where = max(Y1, . . . , Yn).
(a)Find the cumulative distribution function of T and show that T is a pivotal quantity.
(b)Construct a one-sided (1 )-CI of the form (, U ] for based on the pivotal quantity T .
(c)Use the confidence interval constructed in (b) to propose a rejection rule for testing
H0 : = 1 against Ha : < 1 at level 0.05.
(d)Suppose for the test in (c), we no longer specify a particular level and wish to report a p-value instead. Derive the (unobserved random) p-value p as a function of .
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