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Understanding Confidence Intervals in Statistics

Learn about the differences between statistics and parameters, notation, sample size selection, and Bootstrap confidence intervals in statistics. This presentation also covers the importance of the normality assumption in confidence intervals and the distinctions between prediction intervals and tolerance intervals.

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Understanding Confidence Intervals in Statistics

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  1. Additional tips on reading Chapter 7 Warning: The following slides are not a substitute for reading the chapter or for understanding what we did in class already. They are meant to help you get more out of reading the chapter, and they assume you already understand what a CI is!

  2. Notation: Statistics vs. parameters

  3. More notation

  4. More notation

  5. More notation

  6. More notation

  7. Choice of sample size

  8. Choice of sample size, proportions only

  9. Bootstrap CI’s, Section 7.1 • This is a very cool idea. • Don’t worry about it for the purposes of this class.

  10. Difference between CI and UCB • Upper limit, confidence interval: • Upper confidence bound:

  11. CI’s if sample is normal

  12. How important is normality assumption? • Not very important • In other words, you can use this CI without much worry UNLESS the sample is small AND normality is strongly violated. (Concerned? Read up on and use bootstrap technique.) • The formula above is how Minitab calculated your CI’s in the lab.

  13. How important is normality assumption? • Very important • In other words, don’t use this CI unless you’re pretty sure normality is a valid assumption. • Therefore, this isn’t such a useful CI formula.

  14. Prediction intervals vs. Tolerance intervals • Prediction (p. 304): Used to capture a SINGLE future observation with specified confidence level. • Tolerance (p. 305): Used to capture at least a specified proportion of the ENTIRE POPULATION with a specified confidence level. Note: Tolerance intervals require a whole new table (Table A.6). Prediction intervals just use t values.

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