lecture17 - lecture 17, Hypothesis Testing I 1/29 Null and...

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Unformatted text preview: 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 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 , 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 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 : μ ≤ 50 versus H a : μ > 50 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 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 : μ ≥ 19 . 5 versus H a : μ < 19 . 5 lecture 17,...
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lecture17 - lecture 17, Hypothesis Testing I 1/29 Null and...

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