STAT151 Lecture Notes - Lecture 20: Simple Random Sample, Variance, Sampling Distribution
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4 Apr 2018
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STAT151 Full Course Notes
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Section 13 (chapters 21, 22) - inferences for two means: one variable (mean, comparing two population means; two types: Sampling distribution of the difference between two sample means for independent samples: the mean of all possible differences between the two sample means is equal to the difference between the two population means. Sd of y-bar1 - y-bar2 = sum of (population variance / sample size: the difference between two sample means is assumed to be normal. Purpose: to test for the difference between two population means based on two sample means. Assumptions: simple random sampling (implies independent sampling within samples, normal populations or large samples. State null and alternative hypotheses (may be one-, right-, or left-tailed) Calculate test statistic: t = (y-bar1 - y-(cid:271)ar(cid:1006)(cid:895) / (cid:894)(cid:894)sa(cid:373)ple varia(cid:374)(cid:272)e / sa(cid:373)ple size(cid:895)1 + (sample variance / sample size)2: df = minimum of n1 - 1 or n2 - 2. The df always rounds down (sample size rounds up): hypothesized difference is 0.