Consider a random sample of size one (n = 1) from the distribution with probability function [@y(0-1), if 0 0 otherwise. f(y; 0) = 0, (a) To test Ho: 0 = 0, versus H₂ : 0 = 0₁ > 80, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (b) Find the value of k so that at 0 = 2 the size of the test is 5%. (e) Obtain the power function of the test in part (a).

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Consider a random sample of size one (n 1) from the distribution with probability
function
f(y; 0) =
[0y(0-1), if 0 <y<1 for € > 0
[o,
otherwise.
(a) To test Ho: 0 = 0, versus H₁ : 0 = 0 > 00, find a most powerful test. Let the
positive constant to define the rejection region of the test be k.
(b) Find the value of k so that at 0 = 2 the size of the test is 5%.
(c) Obtain the power function of the test in part (a).
Transcribed Image Text:Consider a random sample of size one (n 1) from the distribution with probability function f(y; 0) = [0y(0-1), if 0 <y<1 for € > 0 [o, otherwise. (a) To test Ho: 0 = 0, versus H₁ : 0 = 0 > 00, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (b) Find the value of k so that at 0 = 2 the size of the test is 5%. (c) Obtain the power function of the test in part (a).
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