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Chapter 7 Notes.docx

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Biology 2244A/B
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thBio 2244B Textbook Notes Chapter 7 71 72 73 75 March 13 201271 OverviewDefinitionsHypothesis a claim or statement about a property of a populationHypothesis test test of significance a standard procedure for testing a claim about a property of a populationRecall the rare event rule if under a given assumption the probability of a particular observed event is exceptionally small we conclude that the assumption is probably not correct72 Basics of Hypothesis TestingComponents of a formal hypothesis testoNull hypothesis HA statement that the value of a population parameter such as 0proportion mean or standard deviation is equal to some claimed value We test the null hypothesis directly in the sense that we assume it is true and reach a conclusion to either reject H or fail to reject H00oAlternative hypothesis Hor H the statement that the parameter has a value that 1 asomehow differs from the null hypothesis For this chapter the symbolic form of the alternative hypothesis must use one of these symbolsoror oTest statistic a value computed from the sample data and it is used in making the decision about the rejection of the null hypothesisit is found by converting the sample statistic to a score with the assumption that the null hypothesis is true ppzTest statistic for proportion pqnxxztsTest statistic for meanOR nnTest statistic for standard deviation 2n1s2X2Critical region rejection region the set of all values of the test statistic that cause us to reject the null hypothesisSignificance level a the probability that the test statistic will fall in the critical region when the null hypothesis is actually trueoIf the test statistic falls within the critical region we reject the null hypothesis so a is the probability of making the mistake of rejecting the null hypothesis when it is actually trueCritical value any value that separates the critical region where we reject the null hypothesis from values of the test statistic that do not lead to rejection of the null hypothesis oCritical values depend on the nature of the null hypothesis the sampling distribution that applies and a oSee the figure at right to help determine what critical value to use Tails the extreme regions in a distribution that are bounded by critical valuesoTwotailed test the critical region is in the two extremes of the regions tails under the curve
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