Question: For a 2 2 table, consider H 0 : 11 = 2 , 12 = 21 = (1 ),

For a 2 × 2 table, consider H0: π11 = θ2, π12 = π21 = θ(1 – θ), π22 = (1 – θ)2.

a. Show that the marginal distributions are identical and that independence holds.

b. For a multinomial sample, under H0 show that θ̂ = (p1+ + p+1)/2.

c. Explain how to test H0. Show that df = 2 for the test statistic.

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