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Unformatted text preview: Chapter 16 SinglePopulation Hypothesis Tests Hypothesis Tests A statistical hypothesis is an assumption about a population parameter. There are two types of statistical hypotheses. Null hypothesis  The null hypothesis, H , represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. Alternative hypothesis (Research hypothesis)  The alternative hypothesis, H 1 , is a statement of what a statistical hypothesis test is set up to establish. Hypothesis Tests Examples Trials H : The person is innocent H 1 : The person is guilty Soda H : = 12 oz H 1 : < 12 oz Hypothesis Tests Test Statistics  the random variable X whose value is tested to arrive at a decision. Critical values the values of the test statistic that separate the rejection and nonrejection regions. Rejection Region  the set of values for the test statistic that leads to rejection of H Nonrejection region  the set of values not in the rejection region that leads to nonrejection of H Errors in Hypothesis Tests Actual Situation H is true H is false Decision Reject H Type I error ( ) No error Fail to reject H No error Type II error ( ) 2200 (Significance level): Probability of making Type I error 2200 : Probability of making Type II error 1 : Power of Test (Probability of rejecting H when H is false) Hypothesis Tests Tails of a Test Twotailed Test Lefttailed Test Righttailed Test H = = or = or H 1 < > Rejection region Both tails Left tail Right tail pvalue Sum of areas beyond the test statistics Area to the left of the test statistic Area to the right of the test statistic Hypothesis Tests Examples Twotailed test: According to the US Bureau of the Census, the mean family size was 3.17 in 1991. An economist wants to check whether or not this mean has changed since 1991. 1 /2 /2 C 1 C 2 H : = 3.17 H 1 : 3.17 Nonrejection Region Rejection Region Rejection Region =3.17 Hypothesis Tests Examples Lefttailed test: A softdrink company claims that, on average, its cans contain 12 oz of soda. Suppose that a consumer agency wants to test whether the mean amount of soda per can is less than 12 oz....
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 Fall '11
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