Question: Suppose {Y 1 , . . . , Y n } are IID from Uniform(0, ) Let T = / , where = max( Y

Suppose {Y₁, . . . , Y_n} are IID from Uniform(0,) Let T = /, where = max(Y₁, . . . , Y_n).

(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 H_a : < 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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