Chapter_18 - Chapter 18 Two-Sample Problems BPS - 5th Ed....

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BPS - 5th Ed. Chapter 18 1 Chapter 18 Two-Sample Problems
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BPS - 5th Ed. Chapter 18 2 Two-Sample Problems The goal of inference is to compare the responses to two treatments or to 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.
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BPS - 5th Ed. Chapter 18 3 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 4 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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BPS - 5th Ed. Chapter 18 5 Two-Sample t Procedures In order to perform inference on the difference of two means ( μ 1 2 ), we’ll need the standard deviation of the observed difference : x 1 - x 2 2 2 2 1 2 1 n σ n σ +
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Chapter 18 6 Two-Sample t Procedures Problem: We don’t know the population standard deviations σ 1 and 2 . Solution: Estimate them with s 1 and s 2 . The result is called the standard error , or estimated standard deviation, of the difference in the sample means. =
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Chapter_18 - Chapter 18 Two-Sample Problems BPS - 5th Ed....

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