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Section 9.2: What is a Test of Significance?

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The Reasoning Behind Statistical Tests Statistical inference uses data from a sample to draw conclusions about a population. Tests ask if sample data gives good evidence against a claim.

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Null Hypothesis H o The claim being tested in a statistical test. The test is designed to assess the strength of the evidence against the null hypothesis. Also known as a statement of “no effect” or “no difference”. Will contain a statement of equality (≤, ≥, or =).

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Alternative Hypothesis H a The statement we hope or suspect is true (instead of the null hypothesis). It is the complement of the null hypothesis. Contains a statement of inequality (, or ≠).

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How they write the statements… Null and alternative hypotheses are written with ▫μ (represents the population parameter) and ▫k (represents the claim value) ▫Such as H o : μ ≥ k H a : μ < k

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How would you write it??? A radio station publicizes that its proportion of the local listening audience is greater than 39%. ▫H o : μ ≤ 39% ▫H a : μ > 39% ▫Which was the claim?

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How would you write it??? A consumer analyst reports that the mean life of a certain type of car battery is 74 months. ▫H o : μ = 74 months ▫H a : μ ≠ 74 months ▫Which was the claim here? ▫FYI, the claim will not always be H a.

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Demonstration of H o with Basketball If a basketball coach claims each of his players can hit 80% of their free throws, this is the null hypothesis. We will test this. What is the alternative hypothesis? Demonstration will use activity on www.whfreeman.com/sta www.whfreeman.com/sta After each demonstration, we will also be given their true free throw percentage (which may or may not be 80%).

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Homework Homework will be posted online…worksheet with 6 questions. This is due on block day. Remember, if you weren’t here for the 9.1 quiz, or if I notified you that you were missing another exam, these will all be made up on block day this week before the vacation. I will also distribute the extra credit assignment and/or post it online on block day.

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