UASTAT151Ch9

UASTAT151Ch9 - 9.1 Hypotheses and Test Procedures Defn A...

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9.1 Hypotheses and Test Procedures Def’n: A null hypothesis is a claim about a population parameter that is assumed to be true until it is declared false. An alternative hypothesis is a claim about a population parameter that will be true if the null hypothesis is false. In carrying out a test of H 0 vs. H A , the hypothesis H 0 is “rejected” in favour of H A only if sample evidence strongly suggests that H 0 is false. If the sample does not contain such evidence, H 0 is “not rejected” or you “fail to reject” it. NEVER “accept” H 0 or H A …for different reasons. Ex9.1) H 0 : μ = 2.8 H A : μ 2.8 pop’n characteristic hypothesized value or “claim” Def’n: A two-tailed test has “rejection regions” in both tails. A one-tailed test has a “rejection region” in one tail. A lower-tailed test has the “rejection region” in the left tail. An upper-tailed test has the “rejection region” in the right tail. Ex9.2) a) H 0 : μ = 15 H A : μ = 15 Æ INCORRECT b) H 0 : μ = 123 H A : μ = 125 Æ INCORRECT c) H 0 : μ = 123 H A : μ < 123 Æ CORRECT d) H 0 : p = 0.4 H A : p > 0.6 Æ INCORRECT e) H 0 : p = 1.5 H A : p > 1.5 Æ INCORRECT f) H 0 : p ˆ = 0.1 H A : p ˆ 0.1 Æ INCORRECT Two-Tailed Test Lower-Tailed Test Upper-Tailed Test Sign for H 0 = = or = or Sign for H A < > “Rejection region” In both tails In the left tail In the right tail Ex9.3) Is the mean different than μ 0 ? H 0 : μ = μ 0 H A : μ μ 0 Is the mean lower than μ 0 ? H 0 : μ μ 0 H A : μ < μ 0 Is the mean lower or still the same than μ 0 ? H 0 : μ μ 0 H A : μ > μ 0 Is the mean higher than μ 0 ? H 0 : μ μ 0 H A : μ > μ 0 Def’n: A test statistic is the function of the sample data on which a conclusion to reject or fail to reject H 0 is based. For example, Z and t are test statistics. The p -value is a measure of inconsistency between the hypothesized value for a pop’n characteristic and the observed sample. Assuming H 0 is true, the p -value can be defined as the probability of obtaining a test statistic value at least as inconsistent with H

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UASTAT151Ch9 - 9.1 Hypotheses and Test Procedures Defn A...

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