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# lecture10note - Psych 100A Winter 2010 Lecture 10...

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1 Psych 100A Winter 2010 Lecture 10: Hypothesis testing & Power Analysis 1. Test for , known 2. Computation of power 3. Relationships among , power and n 4. Power curves 12.Tests of significance are about one question and that question is always the same: HT: notations and definitions (continued) “How easy is it to explain the difference How easy is it to explain the difference between the observed data (sample statistic) and the expected outcome (H O ) by chance alone.” 2 3. Theorem: hypothesis test for , 2 known If x 1 , x 2 , …, x n is a random sample from a normal population or a large random sample from any population with known variance 2 , then do O H : A . 2 . 1 : versus n x z TS : . 3 2 . 3 . 2 . 1 : if reject CR error I type 3 Example (Kuzma). Boys of a certain age have a mean weight of 85 lb. A complaint was made that, in a municipal children’s home, the boys are underfed. As one bit of evidence, all 25 boys of a given age were weighed and lb. 94 . 80 Suppose it is known that = 11.6 lb. At a significance level = 0.05, what do you conclude about the complaint? 4 Solution. 1. H O : = 85 lb versus H A : < 85 lb. 2. Data: 3. Assumptions: a. SRS of 25 boys b Weights normally distributed lb. 94 . 80 74 . 1 25 6 . 11 85 95 . 80 b. Weights normally distributed c. = 11.6 lb.

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lecture10note - Psych 100A Winter 2010 Lecture 10...

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