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I S THAT C OIN F AIR ? Section 10.3

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DEFINITIONS Null Hypothesis (H 0 ) : claiming that nothing that is out of the ordinary. Alternative Hypothesis (H 1 ): the complement of the null Confidence Interval: the percentage that you use to determine if your hypothesis is true. Most common CIs :.05,.01,.001 If the probability we are trying to prove and even more extreme probabilities add up to be less than the set confidence interval, reject the null

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E XAMPLE 1 If a coin is tossed 50 times and less than 20 heads or greater than 30 heads occur, is a person justified in thinking the coin is unfair? Test with a.05 confidence level. H 0 = the coin is fair H 1 = the coin is unfair Binomcdf(50, ½, 19) =.0595 1 – binomcdf(50, ½, 30) =.0595.1189 >.05 Cannot reject null hypothesis

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E XAMPLE 2 A coin is tossed 5 times and 5 heads occur. At the.05 level, test the hypothesis that the coin is fair. H 0 = the coin is fair H 1 = the coin is biased Find the probability that either 5 heads occur or 5 tails occur. 2 * binompdf(5, ½, 5).0625 Since.0625 >.05, we cannot reject the null

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E XAMPLE 3 Tickets for two concerts went on sale at the same time. Of the first 30 tickets sold, 12 were for the first concert and 18 for the second. Is the concert hall manager justified in thinking that many more tickets will be sold for the second concert? H 0 = there is an equal probability for each of the concerts H 1 = the second concert will sell more tickets binomcdf(30, ½, 12).1808 Since.1808 >.05; cannot reject

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H OMEWORK Pages 645 – 646 1 – 6, 11, 12

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