chap7a - STATISTICS 211 Prof EMANUEL PARZEN Chapter 7A...

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STATISTICS 211 Prof EMANUEL PARZEN Chapter 7A OUTLINE TWO SAMPLE INFERENCE CASE \mu: Two samples of continuous variable Y Scientific nature of random variable Y being observed Distribution of variable Y: (1) Assume NORMAL or (2) assume finite population means and variances without specifying model for distribution of Y Parameters to estimate and test: population means \mu_1, \mu_2 Hypothesis tests: null hypothesis H_0: \mu_1-\mu_2=c specified constant TEST STATISTIC Z(\mu_1\hat-\mu_2\hat, \mu_1-\mu_2=c)=(\mu_1\hat-\mu_2\hat-c)/S.E. STANDARD ERROR S.E. = S.E.(\mu_1\hat - \mu_2\hat) = sqrt(V), unpooled case when do not assume equal population variances Unpooled formula for ENDPOINT function confidence intervals for mu_1-mu_2: Hypothesis testing applies pooled case formula for S.E. to test null hypothesis then assume equal population variances whose common value is denoted \sigma; Pooled formula to compute S.E S.E.=S.E._pool= S_pool sqrt((1/n_1)+(1/n_2) define (S_pool)^2=((n_1- 1)S_1^2+(n_2_-1)S_2^2)/(n-2)
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