EXAMPLE: We can compute exactp-values in some cases without anormal population. Consider the plebiscite example, where the null isH0:≥.5, which is operationally the same asH0:.5, against thealternativeH1:.5. In the samplen500, we obtained 241 yesvotes, sox̄.482. LetYBinomial500,.5– the distribution of thenumber of yes votes if.5. Then thep-value against.5 isPY≤241. di binomial(500,241,.5).2235647557
∙Thisp-value is probably not small enough to overturn the electionbecause it would entail a chance of Type I error of greater than 22%.∙There is substantially more evidence against the dictator’s claim thatthe population vote was 52.6%.. di binomial(500,241,.526).02715266So we would rejectH0:.526 againstH1:.526 at the 5% levelbut not at the 2.5% level.∙If the dictator cheated, he would arouse less suspicion by reporting apercentage just a little higher than 50%.58
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