On the basis of observations x = (x,x,...,x) from a distribution with density function f(x,0), it...

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On the basis of observations x = (x₁,x₂,...,x) from a distribution with density function f(x,0), it is required to test the hypotheses: Η :θεΦ against H:0εΦ where , and D, are disjoint subsets of the parameter space . Define the respective Type I and Type II error probability functions a(0), 3(0). associated with such a test and show how they are related to the power function K(0). (6 Marks) (ii) What does it mean to say that a test has size a? (3 Marks) On the basis of observations x = (x₁,x₂,...,x) from a distribution with density function f(x,0), it is required to test the hypotheses: Η :θεΦ against H:0εΦ where , and D, are disjoint subsets of the parameter space . Define the respective Type I and Type II error probability functions a(0), 3(0). associated with such a test and show how they are related to the power function K(0). (6 Marks) (ii) What does it mean to say that a test has size a? (3 Marks)