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- 2. Chapter Outline 8.1 Testing the Difference Between Means (Large Independent Samples) 8.2 Testing the Difference Between
- 3. Section 8.1 Testing the Difference Between Means (Large Independent Samples) Larson/Farber 4th ed
- 4. Section 8.1 Objectives Determine whether two samples are independent or dependent Perform a two-sample z-test for
- 5. Two Sample Hypothesis Test Compares two parameters from two populations. Sampling methods: Independent Samples The sample
- 6. Independent and Dependent Samples Independent Samples Sample 1 Sample 2 Dependent Samples Sample 1 Sample 2
- 7. Example: Independent and Dependent Samples Classify the pair of samples as independent or dependent. Sample 1:
- 8. Example: Independent and Dependent Samples Classify the pair of samples as independent or dependent. Sample 1:
- 9. Two Sample Hypothesis Test with Independent Samples Null hypothesis H0 A statistical hypothesis that usually states
- 10. Two Sample Hypothesis Test with Independent Samples H0: μ1 = μ2 Ha: μ1 ≠ μ2 H0:
- 11. Two Sample z-Test for the Difference Between Means Three conditions are necessary to perform a z-test
- 12. Two Sample z-Test for the Difference Between Means If these requirements are met, the sampling distribution
- 13. Two Sample z-Test for the Difference Between Means Test statistic is The standardized test statistic is
- 14. Using a Two-Sample z-Test for the Difference Between Means (Large Independent Samples) State the claim mathematically.
- 15. Using a Two-Sample z-Test for the Difference Between Means (Large Independent Samples) Find the standardized test
- 16. Example: Two-Sample z-Test for the Difference Between Means A consumer education organization claims that there is
- 17. Solution: Two-Sample z-Test for the Difference Between Means H0: Ha: α = n1= , n2 =
- 18. Example: Using Technology to Perform a Two-Sample z-Test The American Automobile Association claims that the average
- 19. Solution: Using Technology to Perform a Two-Sample z-Test H0: Ha: TI-83/84set up: Calculate: Draw: Larson/Farber 4th
- 20. Solution: Using Technology to Perform a Two-Sample z-Test Decision: At the 1% level of significance, there
- 21. Section 8.1 Summary Determined whether two samples are independent or dependent Performed a two-sample z-test for
- 22. Section 8.2 Testing the Difference Between Means (Small Independent Samples) Larson/Farber 4th ed
- 23. Section 8.2 Objectives Perform a t-test for the difference between two means μ1 and μ2 using
- 24. Two Sample t-Test for the Difference Between Means If samples of size less than 30 are
- 25. Two Sample t-Test for the Difference Between Means The standardized test statistic is The standard error
- 26. The standard error for the sampling distribution of is Two Sample t-Test for the Difference Between
- 27. Variances are not equal If the population variances are not equal, then the standard error is
- 28. Normal or t-Distribution? Are both sample sizes at least 30? Are both populations normally distributed? You
- 29. Two-Sample t-Test for the Difference Between Means (Small Independent Samples) State the claim mathematically. Identify the
- 30. Two-Sample t-Test for the Difference Between Means (Small Independent Samples) Determine the rejection region(s). Find the
- 31. Example: Two-Sample t-Test for the Difference Between Means The braking distances of 8 Volkswagen GTIs and
- 32. Solution: Two-Sample t-Test for the Difference Between Means H0: Ha: α = d.f. = Rejection Region:
- 33. Example: Two-Sample t-Test for the Difference Between Means A manufacturer claims that the calling range (in
- 34. Solution: Two-Sample t-Test for the Difference Between Means H0: Ha: α = d.f. = Rejection Region:
- 35. Solution: Two-Sample t-Test for the Difference Between Means Larson/Farber 4th ed
- 36. Solution: Two-Sample t-Test for the Difference Between Means H0: Ha: α = d.f. = Rejection Region:
- 37. Section 8.2 Summary Performed a t-test for the difference between two means μ1 and μ2 using
- 38. Section 8.3 Testing the Difference Between Means (Dependent Samples) Larson/Farber 4th ed
- 39. Section 8.3 Objectives Perform a t-test to test the mean of the difference for a population
- 40. The test statistic is the mean of these differences. t-Test for the Difference Between Means To
- 41. t-Test for the Difference Between Means Three conditions are required to conduct the test. The samples
- 42. Symbols used for the t-Test for μd The number of pairs of data The difference between
- 43. Symbols used for the t-Test for μd The mean of the differences between the paired data
- 44. t-Test for the Difference Between Means The test statistic is The standardized test statistic is The
- 45. t-Test for the Difference Between Means (Dependent Samples) State the claim mathematically. Identify the null and
- 46. t-Test for the Difference Between Means (Dependent Samples) Determine the rejection region(s). Calculate and Use a
- 47. t-Test for the Difference Between Means (Dependent Samples) Make a decision to reject or fail to
- 48. Example: t-Test for the Difference Between Means A golf club manufacturer claims that golfers can lower
- 49. Solution: Two-Sample t-Test for the Difference Between Means H0: Ha: α = d.f. = Rejection Region:
- 50. Solution: Two-Sample t-Test for the Difference Between Means d = (old score) – (new score) Larson/Farber
- 51. Solution: Two-Sample t-Test for the Difference Between Means H0: Ha: α = d.f. = Rejection Region:
- 52. Section 8.3 Summary Performed a t-test to test the mean of the difference for a population
- 53. Section 8.4 Testing the Difference Between Proportions Larson/Farber 4th ed
- 54. Section 8.4 Objectives Perform a z-test for the difference between two population proportions p1 and p2
- 55. Two-Sample z-Test for Proportions Used to test the difference between two population proportions, p1 and p2.
- 56. Two-Sample z-Test for the Difference Between Proportions If these conditions are met, then the sampling distribution
- 57. Two-Sample z-Test for the Difference Between Proportions The test statistic is The standardized test statistic is
- 58. Two-Sample z-Test for the Difference Between Proportions State the claim. Identify the null and alternative hypotheses.
- 59. Two-Sample z-Test for the Difference Between Proportions Find the standardized test statistic. Make a decision to
- 60. Example: Two-Sample z-Test for the Difference Between Proportions In a study of 200 randomly selected adult
- 61. Solution: Two-Sample z-Test for the Difference Between Means H0: Ha: α = n1= , n2 =
- 62. Solution: Two-Sample z-Test for the Difference Between Means Larson/Farber 4th ed
- 63. Solution: Two-Sample z-Test for the Difference Between Means Larson/Farber 4th ed
- 64. Solution: Two-Sample z-Test for the Difference Between Means H0: Ha: α = n1= , n2 =
- 65. Example: Two-Sample z-Test for the Difference Between Proportions A medical research team conducted a study to
- 66. Solution: Two-Sample z-Test for the Difference Between Means H0: Ha: α = n1= , n2 =
- 67. Solution: Two-Sample z-Test for the Difference Between Means Larson/Farber 4th ed
- 68. Solution: Two-Sample z-Test for the Difference Between Means Larson/Farber 4th ed
- 69. Solution: Two-Sample z-Test for the Difference Between Means H0: Ha: α = n1= , n2 =
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