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AP Statistics 11.1 Significance Tests: The Basics Testing a Claim IDEA: Assess the truth of the hypothesis, if true, the other must be false (much like a proof by contradiction). Exercise 11.2 (pg.691) Stating the Hypothesis H0 : The “null hypothesis” no effect or no difference (the claim we are trying to find the evidence AGAINST) Ha : The “alternative hypothesis” the claim we are really trying to find evidence FOR. REMEMBER: Hypotheses always refer to some POPULATION, not a particular outcome. Be sure to state H0 and Ha in terms of the POPULATION and in CONTEXT. Types of Alternative Hypotheses 1. One-sided we are interested in one direction (< , >) 2. Two-sided we are interested in both directions (≠) The “alternative hypothesis (Ha) should express the hopes or suspicions we have BEFORE we see the data. Exercise 11.3 (pg.693) Exercise 11.4 (pg. 693) Conditions for Significance Test 1. SRS 2. Normality 3. Independence Test Statistic = 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆−𝒉𝒚𝒑𝒐𝒕𝒉𝒆𝒔𝒊𝒔 𝒗𝒂𝒍𝒖𝒆 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒅𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝒕𝒉𝒆 𝒆𝒔𝒕𝒊𝒎𝒂𝒕𝒆 P-Value (unlikelihood) The probability, computed assuming the H0 is true, that the observed outcome would take a value as extreme or more extreme than the actual observed is the p-value of the test. NOTE: The smaller the p-value, the stronger the evidence against H0 Exercise 11.8 (pg. 698) Exercise 11.9 (pg.698) Statistical Significance If the p-value is as small as (or smaller) than alpha, , we say the data are statistically significant at level . NOTE: Although there is no “rule”, if a question does not give a specific level for , use =0.05 USING : Declare the level for Test the data Find the p-value Exercise 11.14 (pg. 701) Exercise 11.15 (pg. 701) Exercise 11.16 (pg. 702) 11.19 – 11.26