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Consider a multinomial distribution with four cells, sample size n, and probability vector ((1 − p),...

Consider a multinomial distribution with four cells, sample size n, and probability vector ((1 − p), p(1 − p), p2 (1 − p), p3 ) for some unknown probability p, 0 < p < 1. Let nj be the number of observations that fall in cell j. Test the hypothesis that H0 : p = 0.6. What is the test statistic and the asymptotic distribution under this hypothesis?

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Answer #1

It is a multinomial distribution with 4 cells, so at first, we will find p1, p2, p3, p4 where p = 0.6.

Under the H0, it has an asymptotical chi-square distribution with the 3 degrees of freedom.

it got a degree of freedom = 3.

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