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Unformatted text preview: 5. Hypothesis Testing Dave Goldsman Georgia Institute of Technology, Atlanta, GA, USA 8/21/10 Goldsman 8/21/10 1 / 64 Outline 1 Introduction to Hypothesis Testing 2 Normal Mean Tests (variance known) Simple Hypothesis Test Test Design TwoSample Normal Mean Tests 3 Normal Mean Tests (variance unknown) Simple Hypothesis Test TwoSample Normal Mean Tests Pooled tTest Approximate tTest Paired tTest 4 Other Hypothesis Tests Normal Variance Test TwoSample Test for Equal Variances Bernoulli Proportion Test Goldsman 8/21/10 2 / 64 Introduction to Hypothesis Testing Introduction to Hypothesis Testing General Approach 1. State a hypothesis. 2. Select a test statistic (to test whether or not the hypothesis is true). 3. Evaluate (calculate) the test statistic. 4. Interpret results does the test statistic allow you to reject your hypothesis? Details follow. . . Goldsman 8/21/10 3 / 64 Introduction to Hypothesis Testing 1. Hypotheses are simply statements or claims about parameter values. You perform a hypothesis test to prove or disprove the claim. Set up a null hypothesis ( H ) and an alternative hypothesis ( H 1 ) to cover the entire parameter space. The null hyp sort of represents the status quo. Example: We claim that the mean weight of a filled package of chicken is ounces. (We specify .) H : = H 1 : negationslash = This is a twosided test . Well reject the claim if (an estimator of ) is too high or too small. Goldsman 8/21/10 4 / 64 Introduction to Hypothesis Testing Example: We claim that a certain brand of tires lasts for at least a mean of miles. (We specify .) H : H 1 : < This is a onesided test . Well reject the claim if is too small. Example: We claim that emissions from a certain type of car do not exceed a mean of ppm. (We specify .) H : H 1 : > This is a onesided test . Well reject the claim if is too large. Goldsman 8/21/10 5 / 64 Introduction to Hypothesis Testing Idea: H is the old, conservative status quo. H 1 is the new, radical hypothesis. Although you may not be toooo sure about the truth of H , you wont reject it in favor of H 1 unless you see substantial evidence in support of H 1 . Innocent until proven guilty. If you get substantial evidence supporting H 1 , youll decide to reject H . Otherwise, you fail to reject H . (This roughly means that you grudgingly accept H .) Goldsman 8/21/10 6 / 64 Introduction to Hypothesis Testing 2. Select a test statistic (to test if H is true). For instance, we could compare an estimator with . The comparison is accomplished using a known sampling distribution (aka test statistic), e.g., z obs = X / n (if 2 is known) or t obs = X S/ n (if 2 is unknown) Lots more details later....
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This note was uploaded on 08/27/2011 for the course ISYE 3770 taught by Professor Goldsman during the Spring '07 term at Georgia Institute of Technology.
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