Let X be and suppose that it is desired to test versus (Imagine that it is known that 8 is one of these two values.) Consider the test which accepts Ho if x 50, and randomly chooses Ho or HI (with...

Let X be

and suppose that it is desired to test

versus

(Imagine that it is known that 8 is one of these two values.) Consider the test which accepts Ho if x <> 50, and randomly chooses Ho or HI (with probability! each) when x = 50.

(a) Calculato the probabilities of Type I and Type II error for this test. (Since these error probabilities are the same, their common value could be considered to be the overall frequentist error probability for the test.)

(b) If x = 50 is observed, what is the intuitive (conditional) probability of actually making an error in use of the test.