chap16_2010 - Chapter 16 Single-Population Hypothesis Tests...

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Chapter 16 Single-Population Hypothesis Tests
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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 0 , 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.
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Hypothesis Tests Examples Trials – H 0 : The person is innocent – H 1 : The person is guilty Soda – H 0 : μ = 12 oz – H 1 : μ < 12 oz
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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 non-rejection regions. Rejection Region -- the set of values for the test statistic that leads to rejection of H 0 Non-rejection region -- the set of values not in the rejection region that leads to non-rejection of H 0
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Errors in Hypothesis Tests Actual Situation H 0 is true H 0 is false Decision Reject H 0 Type I error ( α ) No error Fail to reject H 0 No error Type II error ( β ) 2200 α (Significance level): Probability of making Type I error 2200 β : Probability of making Type II error 1- β : Power of Test (Probability of rejecting H 0 when H 0 is false)
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Hypothesis Tests Tails of a Test Two-tailed Test Left-tailed Test Right-tailed Test H 0 = = or = or H 1 < > Rejection region Both tails Left tail Right tail p-value Sum of areas beyond the test statistics Area to the left of the test statistic Area to the right of the test statistic
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Hypothesis Tests Examples Two-tailed 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- α α /2 α /2 C 1 C 2 H 0 : μ = 3.17 H 1 : μ 3.17 Non-rejection Region Rejection Region Rejection Region μ =3.17
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Hypothesis Tests Examples Left-tailed test: A soft-drink 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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