Let Y i be a bin(n i , i ) variate for group i, i =
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Let Yi be a bin(ni, πi) variate for group i, i = 1, ...... N, with {Yi} independent. Consider the model that π1 = .... = πN. Denote that common value by π. For observations {yi} show that π̂ = (∑yi)/(∑ni).
When all ni = 1, for testing this model’s fit in the N × 2 table, show that X2 = n. Thus, goodness-of-fit statistics can be completely uninformative for ungrouped data.
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From the product of the N binomial mass functions the model is then equivalent to having a si...View the full answer
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