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AP STATISTICS REVIEW INFERENCE

AP STATISTICS REVIEW INFERENCE. Statistical Inference. Drawing conclusions (“to infer”) about a population based upon data from a sample. Two types of inference: Confidence intervals Significance tests. USB DocumentsAP STATISTICSquick guide to inference.pdf. Confidence Intervals.

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AP STATISTICS REVIEW INFERENCE

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  1. AP STATISTICSREVIEWINFERENCE

  2. Statistical Inference • Drawing conclusions (“to infer”) about a population based upon data from a sample. • Two types of inference: • Confidence intervals • Significance tests USB Documents\AP STATISTICS\quick guide to inference.pdf

  3. Confidence Intervals Confidence intervals estimate the true value of the parameter where the parameter is the true mean , true proportion p, or true slope .

  4. Confidence Intervals • 1-sample t-interval for • 2-sample t-interval for • Matched-pairs t-interval • 1-proportion z-interval for p • 2-proportion z-interval for p1 - p2 • t-interval for slope

  5. Confidence Intervals P A C S = Parameters = Assumptions (conditions) = Calculate interval = State a conclusion

  6. Interpret the confidence level: C% of all intervals produced using this method will capture the true mean (difference in means), or proportion (difference in proportions), or slope. (Describe the parameter in context!)

  7. Interpret the confidence interval: I am C% confident that the true parameter (insert context) is between ___ and ___ (insert units), based on this sample.

  8. (2000) Question 6 A random sample of 400 married couples was selected from a large population of married couples. • Heights of married men are approximately normally distributed with a mean 70 inches and standard deviation 3 inches. • Heights of married women are approximately normally distributed with mean 65 inches and standard deviation 2.5 inches. • There were 20 couples in which the wife was taller than her husband, and there were 380 couples in which the wife was shorter than her husband. • Find a 95 percent confidence interval for the proportion of married couples in the population for which the wife is taller than her husband. Interpret your interval in the context of this question.

  9. Solution (2000 – Question 6, part a) Assumption: large sample size since Parameter, Assumptions, Test Name (or formula): p = true proportion of married couples in which the wife is taller than her husband 1-proportion z-interval for p

  10. Solution (2000 – Question 6, part a) Calculations:

  11. Solution (2000 – Question 6, part a) Interpret the interval: I am 95% confident that the true proportion of couples in which the wife is taller than her husband is between .028 and .071, based on this sample. USB Documents\AP STATISTICS\AP Stats\correct & incorrect ways to explain CI.doc

  12. Significance Tests H A T S = Hypothesis (define parameters!) = Assumptions (conditions) = Test name or formula = State a conclusion

  13. Significance Tests Significance tests provide evidence for some claim using sample data. test statistic = estimated value – hypothesized value standard error of the estimate

  14. Significance Tests • 1-sample t-test for • 2-sample t-test for • Matched pairs t-test • 1-proportion z-test for p • 2-proportion z-test for p1 – p2 • Chi-square goodness-of-fit test • Chi-square test for homogeneity or independence/association • t-test for slope 

  15. What is the P-value? The P-value is the probability of getting an observation as extreme or even more extreme by chance alone, assuming that the null hypothesis is true. If the P-value is small (< alpha), then we reject Ho and accept Ha. (Results are statistically significant) If the P-value is large (> alpha), then we fail to reject Ho and fail to accept Ha. (Results are not statistically significant)

  16. Know your inference procedures Helpful web site: http://www.ltcconline.net/greenl/java/Statistics/StatsMatch/StatsMatch.htm

  17. (2000) Question 4

  18. Solution (2000) Question 4

  19. Solution (2000) Question 4

  20. Solution (2000) Question 4

  21. Solution (2000) Question 4

  22. Solution (2000) Question 4

  23. Solution (2000) Question 4

  24. Scoring (2000) Question 4

  25. Scoring (2000) Question 4

  26. (2003) Question 5

  27. Solution (2003) Question 5

  28. Solution (2003) Question 5

  29. Solution (2003) Question 5

  30. Solution (2003) Question 5

  31. Scoring (2003) Question 5

  32. Type I, Type II Errors & Power • Type I Error () Ho is true, but we reject Ho (& support Ha) • Type II Error () Ho is false, but we fail to reject Ho (& fail to support Ha) • Power (1- ) the probability of correctly rejecting Ho

  33. Type I, Type II Errors & Power

  34. How to increase power: • Increase alpha (level of significance) • Increase the sample size, n • Decrease variability • Increase the magnitude of the effect (the difference in the hypothesized value of a parameter & its true value

  35. (2003) Question 2

  36. Solution (2003) Question 2

  37. Solution (2003) Question 2

  38. Solution (2003) Question 2

  39. Scoring (2003) Question 2

  40. Scoring (2003) Question 2

  41. Scoring (2003) Question 2

  42. Scoring (2003) Question 2

  43. Good Luck!

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