Problem 1 The random variable can take one of five values: (x1, r2, 23, a4,5]. T

Question

Problem 1 The random variable can take one of five values: (x1, r2, 23, a4,5]. The null hypothesis Ho gives the probabilities in the table below. The alternative hypothesis Hi says that the probability distribution is one of three possibilities H1,1, H1,2, or H1,3, as shoun in the table below. 0.05 0.2 0.1 0.2 2 0.25 0.3 0.3 0.2 3 0.35 0.3 0.2 0.3 4 0.15 0.1 0.1 0.1 s 0.2 0.1 0.3 0.2 (a) For each of the values of X, find the likelihood ratio A., and rank the X values accordingly. (b) For each of the values of X, find the likelihood ratio A, and Tank the X values accordingly. Note that nin(A,1). (c) What values of are possible under a generalized likelihood rto test? (d) Find the rejection region for the Generalized likelihood ratio test that has 0.25. (e) Find the power of that test, assuming Hh,a (f) Find the p-value of a result of z2.

Explanation / Answer

A) X1=.05/(.2+.1+.2)=.1

X2=.25/(.3+3+.2)=.3125

X3=.35/(.3+.2+.3)=.4375

X4=.15/(.1+.1+.1)=.5

X5=.2/(.1+.3+.2)=.33

X4>X3>X5>X2>X1

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