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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 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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