b) Let X to be a random sample from a distribution with a probability density function given by f(x; 0) = {0x0-¹, if 0 < x < 1, 0 € {1,2}, elsewhere It is desired to test a null hypothesis Ho: 0 = 1 against the alternative hypothesis H₁:0 = 2. Suppose that the test rejects H₁ if x ≥ √√3 i) Find the level of significance of the test, a. ii) Calculate the power of the test.

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b) Let X to be a random sample from a distribution with a probability density function given by
f(x; 0) = {0x²
(0x0-1, if 0<x< 1, 0 € {1,2},
elsewhere
It is desired to test a null hypothesis Ho: 0 = 1 against the alternative hypothesis H₁:0 = 2.
Suppose that the test rejects H, if x ≥
i) Find the level of significance of the test, a.
ii) Calculate the power of the test.
Transcribed Image Text:b) Let X to be a random sample from a distribution with a probability density function given by f(x; 0) = {0x² (0x0-1, if 0<x< 1, 0 € {1,2}, elsewhere It is desired to test a null hypothesis Ho: 0 = 1 against the alternative hypothesis H₁:0 = 2. Suppose that the test rejects H, if x ≥ i) Find the level of significance of the test, a. ii) Calculate the power of the test.
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We have to find

a.. Level of significance

b..power of test 

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