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class 19 - Inferences About Means Click to edit Master...

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Click to edit Master subtitle style 11/13/10 Inferences About Means
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11/13/10 2Slide 1- 2 Getting Started Now that we know how to create confidence intervals and test hypotheses about proportions, it’d be nice to be able to do the same for means. Just as we did before, we will base both our confidence interval and our hypothesis test on the sampling distribution model.
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11/13/10 3Slide 1- 3 All we need is a random sample of quantitative data. And the true population standard deviation, σ . But how do we find this? Getting Started (cont.)
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11/13/10 4Slide 1- 4 Getting Started (cont.) Proportions have a link between the proportion value and the standard deviation of the sample proportion. This is not the case with means— knowing the sample mean tells us nothing about We’ll do the best we can: estimate the population parameter σ with the sample statistic s .
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11/13/10 5Slide 1- 5 Getting Started (cont.) We now have extra variation in our standard error from s , the sample standard deviation. We need to allow for the extra variation so that it does not mess up the margin of error and P-value, especially for a small sample. And, the shape of the sampling model changes—the model is no longer Normal. So, what is the
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11/13/10 6Slide 1- 6 Gosset’s t William S. Gosset figured out what the sampling model was. The sampling model that Gosset found is often known as Student’s t . The Student’s t -models form a whole family of related distributions that depend on a parameter known as degrees of freedom . We often denote degrees of freedom as df , and the model as tdf .
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11/13/10 7Slide 1- 7 A Confidence Interval for Means? A practical sampling distribution model for means When the conditions are met, the standardized sample mean follows a Student’s t -model with n – 1 degrees of freedom. We estimate the standard error with
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11/13/10 8Slide 1- 8 When Gosset corrected the model for the extra uncertainty, the margin of error got bigger.
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