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Unformatted text preview: Inferences from two samples (Sections 9.3, 9.4, 10.3) Some new concepts The framework: Until now we had one population, one random sample from that population and just one parameter ( or ) with an unknown value and we made inference about the unknown value of the parameter. In this Chapter We have two populations, a population of Xs [say, {X 1 , X 2 , , X N } ] and a population of Ys, [say, {Y 1 , Y 2 , , Y M }]. If X and Y are both quantitative variables, the population means are X and Y , and standard deviations are X and Y , respectively; we are interested in making inferences about the difference of population means, X Y . If both X and Y are categorical variables, each with two categories, then the parameter of interest is the difference between the proportion of Successs, denoted by X , in the population of Xs and proportion of Successs, denoted by Y in the population of Ys. We select (simple) random sample of size n X from the population of Xs and a (simple) random sample of size n Y from the population of Ys to make inferences about the difference of the parameters of interest in the respective populations. The samples can be either independent of each other or they may be dependent on each other. Definition: Two random samples are said to be independent samples if the selection of a unit from one population has no effect on the selection or nonselection of another unit from the second population. Otherwise the samples are said to be dependent samples. Independent samples are used in most applications. However, in some applications the selection of one unit will from one of the populations determines the selection of another one from the second population. Such samples are said to be dependent samples. In such applications one unit from each population make up a pair. Thus we have a random sample of pairs . These pairs either come naturally (e.g., twinsstudies, studies of married couples, observations on the same person under two different conditions, etc.) or the pairs are created by the experimenter, being matched on as many characteristics as possible, except the one characteristic of interest to the researcher. In many experiments the same population unit is used as its pair (before after studies). STA 3032 Chap 6 Part 2, Page 1 of 20 Point Estimation: The following table gives difference of two population parameters and their point estimators: Difference of Two Population Parameters Estimators of the Difference of Two Population Parameters 1 2  = Difference of two population means 1 2 1 2 X X  = = Difference of the two sample means p 1 p 2 = Difference of two population proportions 1 2 1 2 p p p p = = Difference of two Sample proportions We have the usual general formula for confidence intervals and the six steps of hypothesis testing....
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 Fall '08
 Kyung

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