1.33 For testing Ho: ; = jo, j = 1,..., c, using sample multinomial proportions {;}, the...
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1.33 For testing Ho: π; = πjo, j = 1,...,
c, using sample multinomial proportions {;}, the likelihood-ratio statistic (1.17) is 2
G² = −2η Σπ; log(njo/nj).
j j
Show that G² ≥ 0, with equality if and only if ₁ = πjo for all j. [Hint: Apply Jensen's inequality to E(-2n log X), where X equals πο/π; with probability ;.]
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