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Chapter 18 - STAT 2053 Elementary Statistics Chapter 18...

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STAT 2053 – Elementary Statistics Chapter 18 – Two-Sample Problems 1
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Chapter 18 Chapters 14, 15, and 17 talked about inference methods when we have only one population. In Chapter 18, we are going to use inference to compare two different populations. We may want to compare the effects of two treatments, or compare the characteristics of two populations. We have a separate sample from each treatment or each population. Each sample is separate. The units are not matched, and the samples can be of differing sizes. 2
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Chapter 18 Examples : Do men perform better than women on an exam? Does one drug work faster than another drug? Which advertising campaign brings in more business? These types of problems are everywhere! 3
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BPS - 5th Ed. Chapter 18 4 Case Study Exercise and Pulse Rates A study if performed to compare the mean resting pulse rate of adult subjects who regularly exercise to the mean resting pulse rate of those who do not regularly exercise. This is an example of when to use the two-sample t procedures. n mean std. dev. Exercisers 29 66 8.6 Nonexercisers 31 75 9.0
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BPS - 5th Ed. Chapter 18 5 Conditions for Comparing Two Means We have two independent SRSs , from two distinct populations that is, one sample has no influence on the other--matching violates independence we measure the same variable for both samples. Both populations are Normally distributed the means and standard deviations of the populations are unknown in practice, it is enough that the distributions have similar shapes and that the data have no strong outliers.
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Two Population Means For each population we measure a variable. We call the variable from the first population x 1 , and the one from the second population x 2 . 6 Populati on Variable Mean Std. Dev. 1 x 1 μ 1 σ 1 2 x 2 μ 2 σ 2
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Two Population Means When we compare two population means, we’re most interested in the difference between the means 1 – μ 2 ), or whether or not they are equal.
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