Compare the mean height, μ 1 , of indi- viduals in one...

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Stat 260 - Lecture 29 Recap of Last Class : We derived a large sample Z-test for a population proportion. Test procedure for the mean of a normal population that is valid even when n is small. Today: We will consider inferences based on two independent samples taken from two separate populations.
Inferences Based on Two Samples We have been developing methods for pro- ducing confidence intervals and doing test of hypothesis when interest lies in a single population parameter, e.g. a population mean μ or proportion p . Most often there are two (or more) popu- lations of interest and we wish to compare certain parameters across the two popula- tions. Examples: 1. Compare the mean height, μ 1 , of indi- viduals in one population to the mean height, μ 2 , of individuals in a separate population. 2. Compare the proportion of males, p 1 , in one population to the proportion of males in some other population p 2 .
Z-tests and CI’s for a Difference Be- tween Two Means Assume there are two separate populations and the variable of interest has mean μ 1 in the first population and mean μ 2 in the second population. The parameter θ defined by θ = μ 1 - μ 2 is often of interest when we want to com- pare the two populations. When μ 1 - μ 2 = 0, the populations are iden- tical with respect to their means.
Upon obtaining a sample from population 1 and another sample from population 2, we would like to test hypotheses and con- struct confidence intervals for the unknown

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