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Unformatted text preview: Stat 104 Section 7 Josh Zagorsky < [email protected] > Hypothesis Testing Concepts 1. The Null Hypothesis says that the parameter is unchanged. Finding a statistically significant difference means rejecting the null hypothesis and accepting an alternative hypothesis. H : μ = μ One-sided H a : μ > μ or H a : μ < μ . Two-sided H a : μ 6 = μ 2. Type I Error: Null hypothesis incorrectly rejected (bad) 3. Type II Error: Null hypothesis incorrectly retained (somewhat less bad) 4. Usually use Significance Level α = P ( TypeIError ) = 0 . 05 5. Basic idea of a test statistic: Y- E ( Y | H true ) sd ( Y | H true ) Tests 1. One-sample tests are used for comparing one sample to a declared population statistic. For a mean : t = ¯ X- μ s/ √ n z test is the same, but used when σ (population std. dev.) is known and can be used instead of s (the sample std. dev.). ttest variable==100 (where 100 is replaced by μ ) For a proportion : T = ˆ p- p p p (1- p ) /n prtest variable==0.5 (where 0.5 is replaced by p ) 2. Two-sample tests are used for comparing two separate samples....
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.
- Fall '11