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# lecture17 - lecture 17 Hypothesis Testing I lecture 17...

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lecture 17, Hypothesis Testing I 1 / 29 Null and Alternative Hypotheses and Errors in Hypothesis Testing z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach lecture 17, Hypothesis Testing I Outline 1 Null and Alternative Hypotheses and Errors in Hypothesis Testing 2 z Tests about a Population Mean: σ Known 3 Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach

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lecture 17, Hypothesis Testing I 2 / 29 Null and Alternative Hypotheses and Errors in Hypothesis Testing z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach lecture 17, Hypothesis Testing I Null and Alternative Hypotheses and Errors in Hypothesis Testing Null and Alternative Hypotheses The null hypothesis, denoted H 0 , is a statement of the basic proposition being tested. The statement generally represents the status quo 1 and is not rejected unless there is convincing sample evidence that it is false. the presumption of innocence: the defendant is innocent. This presumption is not rejected unless there’s compelling evidence of guilty. The alternative or research hypothesis, denoted H a , is an alternative to the null hypothesis statement. the defendant is guilty. 1 the current or existing state of affairs
lecture 17, Hypothesis Testing I 3 / 29 Null and Alternative Hypotheses and Errors in Hypothesis Testing z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach lecture 17, Hypothesis Testing I Null and Alternative Hypotheses and Errors in Hypothesis Testing Example: Trash Bag Case Tests show the trash bag has a mean breaking strength μ close to but not exceeding 50 lbs The new bag’s mean breaking strength is not known and is in question, but it is hoped it is stronger than the current one I The null hypothesis H 0 is that the new bag has a mean breaking strength that is 50 lbs or less I The alternative hypothesis H a is that the new bag has a mean breaking strength that exceeds 50 lbs One-sided, “greater than” alternative: H 0 : μ 50 versus H a : μ > 50

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lecture 17, Hypothesis Testing I 4 / 29 Null and Alternative Hypotheses and Errors in Hypothesis Testing z Tests about a Population Mean: σ Known Testing a “Greater Than” Alternative Critical Value Rule The p -value Approach lecture 17, Hypothesis Testing I Null and Alternative Hypotheses and Errors in Hypothesis Testing Example: Payment Time Case With old billing system, the mean bill payment time μ was close to but not less than 39 days It is hoped that the new billing system will reduce the mean bill payment time by more than 50% I The null hypothesis H 0 is that the new billing system has a mean payment time 19.5 days I Alternative hypothesis H a is the new billing system has a mean payment time 19.5 days One-sided, “less than” alternative: H 0 : μ 19 . 5 versus H a : μ < 19 . 5
lecture 17, Hypothesis Testing I 5 / 29

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