Section 9.2: What is a Test of Significance? 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. Null Hypothesis Ho • 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 =). Alternative Hypothesis Ha • 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 ≠). 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 Ho: μ ≥ k Ha : μ < k How would you write it??? • A radio station publicizes that its proportion of the local listening audience is greater than 39%. ▫ Ho: μ ≤ 39% ▫ Ha: μ > 39% ▫ Which was the claim? How would you write it??? • A consumer analyst reports that the mean life of a certain type of car battery is 74 months. ▫ Ho: μ = 74 months ▫ Ha: μ ≠ 74 months ▫ Which was the claim here? ▫ FYI, the claim will not always be Ha. Demonstration of Ho 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 • After each demonstration, we will also be given their true free throw percentage (which may or may not be 80%). 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.