Fora c-category variable,considertesting H0: 1 = 10, ...,c = c0 when counts (y1, ...,yc) haveamultinomialdistribution(2.14)with n =
Question:
Fora c-category variable,considertesting H0: π1 = π10, ...,πc = πc0 when counts (y1, ...,yc)
haveamultinomialdistribution(2.14)with n = Σj yj .
(a) UsingtheresultthattheMLestimateof πj is the jth sampleproportion yj~n, showthat the likelihood-ratiostatisticfortesting H0 is
with df = c−1 for thelarge-samplechi-squareddistribution. The correspondingPearson statistic is X2 = Σj[(yj − nπj0)2]~(nπj0).
(b) Fortestingthatthesixsidesofadiceareequallylikely,werollthedice100times and obtainscounts(15,20,13,14,17,21)foroutcomes(1,2,3,4,5,6).Conductthe likelihood-ratiotestandinterpretthe P-value.
(c) Simulatetheexactsamplingdistributionofthelikelihood-ratiostatisticin(b),anduse it topreciselyapproximatetheexact P-valueofthetestforthedatashown.
Step by Step Answer:
Foundations Of Statistics For Data Scientists With R And Python
ISBN: 9780367748456
1st Edition
Authors: Alan Agresti