State derive the power function for the test


Let X1, ... Xn be a random sample of size n from an exponential distribution, Xi ~ EXP (1,eta). A test of Ho: eta < or equal to eta(not) versus Ha: eta > eta(not) is desired, based on X1:n.

a) Find a critical region of size alpha of the form {x1:n > or equal to c}.

b) Derive the power function for the test of a).

c) Derive a formula to determine the sample size n for a test of size alpha with B = P[TII] if eta = eta1.

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