02-review2-handout

02-review2-handout - STA 3024: Review of STA 2023 (Part 2,...

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STA 3024: Review of STA 2023 (Part 2, Statistical Inference) Douglas Whitaker Statistics Department 11 January 2012 Douglas Whitaker (Statistics Department) 11 January 2012 1 / 57
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Focal Points What is statistical inference? What is a p -value? How is a confidence interval interpreted? Douglas Whitaker (Statistics Department) 11 January 2012 2 / 57
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Goals Now we’re going to review statistical inference . Statistical inference is the term for a set of tools that we use to make conclusions or decisions about a population based on information gathered from a sample of that population. We’ll learn about hypothesis tests and confidence intervals for each situation at the same time. Douglas Whitaker (Statistics Department) 11 January 2012 3 / 57
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Hypothesis Tests vs. Confidence Intervals Definition Very briefly, hypothesis tests are tools used to evaluate a statement about a population (seeing if a specific guess is good or not) Definition confidence intervals are tools used to make guesses about the true population value based on the sample/data. Confidence intervals are a range of guesses. Douglas Whitaker (Statistics Department) 11 January 2012 4 / 57
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Different Types of Hypothesis Tests We’re going to learn/review several types of hypothesis tests now. We’re going to talk about when we can use each one and how to perform it. The major situations that we’ll cover are: one-sample proportions two-sample proportions (independent groups) one-sample means two-sample means (dependent, matched pairs) two-sample means (independent) two-sample means (dependent, matched pairs, nonparametric) two-sample means (independent, nonparametric) The first 5 will be review of Chapters 9 and 10, while the last two are new and from Chapter 15. Douglas Whitaker (Statistics Department) 11 January 2012 5 / 57
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First Exam The first “review” exam will cover all of this material, including the new Chapter 15 material. Douglas Whitaker (Statistics Department) 11 January 2012 6 / 57
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One-Sample Proportions The first thing we’ll care about is making a conclusion about the true population proportion based on one-sample. Example : In 2000, the GSS asked subjects if they would be willing to pay much higher prices in order to protect the environment. Of n = 1154 respondents, 518 indicated a willingness to do so. We care about the true population proportion of people willing to pay more . Douglas Whitaker (Statistics Department) 11 January 2012 7 / 57
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One-Sample Proportions We could ask a few questions based on the example: Is there evidence that less than 47% of people would be willing to pay more? (hypothesis test) Based on the data, what is a good guess for the true proportion of people that are willing to pay more? (confidence interval) We can use hypothesis tests to evaluate any guess, not just “obvious” ones like 50%. “Is there evidence that more than 99.5% of people would be willing to pay more?”. Kind of silly, particularly based on the data, but we can do it.
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02-review2-handout - STA 3024: Review of STA 2023 (Part 2,...

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