1 / 41

Chi-Square (  2 ) Test of Variance

Chi-Square (  2 ) Test of Variance. Chi-Square (  2 ) Test for Variance. 1. Tests One Population Variance or Standard Deviation 2. Assumes Population Is Approximately Normally Distributed 3. Null Hypothesis Is H 0 :  2 =  0 2. Chi-Square (  2 ) Test for Variance.

quinlan-roberts
Télécharger la présentation

Chi-Square (  2 ) Test of Variance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chi-Square (2) Test of Variance

  2. Chi-Square (2) Testfor Variance • 1. Tests One Population Variance or Standard Deviation • 2. Assumes Population Is Approximately Normally Distributed • 3. Null Hypothesis Is H0: 2 = 02

  3. Chi-Square (2) Testfor Variance • 1. Tests One Population Variance or Standard Deviation • 2. Assumes Population Is Approximately Normally Distributed • 3. Null Hypothesis Is H0: 2 = 02 • 4. Test Statistic 2 (n  1)  S Sample Variance 2   2  Hypothesized Pop. Variance 0

  4. Chi-Square (2) Distribution

  5. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?

  6. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05? 2 Table (Portion)

  7. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 2 Table (Portion)

  8. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 2 Table (Portion)

  9. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 2 Table (Portion)

  10. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 2 Table (Portion)

  11. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 df = n - 1 = 2 2 Table (Portion)

  12. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 df = n - 1 = 2 2 Table (Portion)

  13. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 df = n - 1 = 2 2 Table (Portion)

  14. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 df = n - 1 = 2 2 Table (Portion)

  15. Finding Critical Value Example What is the critical 2 value given:Ha: 2 > 0.7n = 3 =.05?  = .05 df = n - 1 = 2 2 Table (Portion)

  16. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? What Do You Do If the Rejection Region Is on the Left?

  17. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? 2 Table (Portion)

  18. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? Reject  = .05 2 Table (Portion)

  19. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? Upper Tail Area for Lower Critical Value = 1-.05 = .95 Reject  = .05 2 Table (Portion)

  20. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? Upper Tail Area for Lower Critical Value = 1-.05 = .95 Reject  = .05 2 Table (Portion)

  21. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? Upper Tail Area for Lower Critical Value = 1-.05 = .95 Reject  = .05 df = n - 1 = 2 2 Table (Portion)

  22. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? Upper Tail Area for Lower Critical Value = 1-.05 = .95 Reject  = .05 df = n - 1 = 2 2 Table (Portion)

  23. Finding Critical Value Example What is the critical 2 value given:Ha: 2< 0.7n = 3 =.05? Upper Tail Area for Lower Critical Value = 1-.05 = .95 Reject  = .05 df = n - 1 = 2 2 Table (Portion)

  24. Chi-Square (2) Test Example • Is the variation in boxes of cereal, measured by the variance, equal to 15 grams? A random sample of 25 boxes had a standard deviation of17.7 grams. Test at the .05 level.

  25. Chi-Square (2) Test Solution • H0: • Ha: •  = • df = • Critical Value(s): Test Statistic: Decision: Conclusion: 2  0

  26. Chi-Square (2) Test Solution • H0: 2 = 15 • Ha: 2 15 •  = • df = • Critical Value(s): Test Statistic: Decision: Conclusion: 2  0

  27. Chi-Square (2) Test Solution • H0: 2 = 15 • Ha: 2 15 •  = .05 • df = 25 - 1 = 24 • Critical Value(s): Test Statistic: Decision: Conclusion: 2  0

  28. Chi-Square (2) Test Solution • H0: 2 = 15 • Ha: 2 15 •  = .05 • df = 25 - 1 = 24 • Critical Value(s): Test Statistic: Decision: Conclusion:  /2 = .025 2  0

  29. Chi-Square (2) Test Solution • H0: 2 = 15 • Ha: 2 15 •  = .05 • df = 25 - 1 = 24 • Critical Value(s): Test Statistic: Decision: Conclusion:  /2 = .025 2  0 12.401 39.364

  30. Chi-Square (2) Test Solution • H0: 2 = 15 • Ha: 2 15 •  = .05 • df = 25 - 1 = 24 • Critical Value(s): Test Statistic: Decision: Conclusion: 2 2 (n  1)  S (25 - 1)  17 . 7 2    2 2 15  0  33 . 42  /2 = .025 2  0 12.401 39.364

  31. Chi-Square (2) Test Solution • H0: 2 = 15 • Ha: 2 15 •  = .05 • df = 25 - 1 = 24 • Critical Value(s): Test Statistic: Decision: Conclusion: 2 2 (n  1)  S (25 - 1)  17 . 7 2    2 2 15  0  33 . 42 Do Not Reject at  = .05  /2 = .025 2  0 12.401 39.364

  32. Chi-Square (2) Test Solution • H0: 2 = 15 • Ha: 2 15 •  = .05 • df = 25 - 1 = 24 • Critical Value(s): Test Statistic: Decision: Conclusion: 2 2 (n  1)  S (25 - 1)  17 . 7 2    2 2 15  0  33 . 42 Do Not Reject at  = .05  /2 = .025 There Is No Evidence 2 Is Not 15 2  0 12.401 39.364

  33. Calculating Type II Error Probabilities

  34. Power of Test • 1. Probability of Rejecting False H0 • Correct Decision • 2. Designated 1 -  • 3. Used in Determining Test Adequacy • 4. Affected by • True Value of Population Parameter • Significance Level  • Standard Deviation & Sample Size n

  35. Finding PowerStep 1 Reject  n =15/25 Hypothesis:H0: 0 368H1: 0 < 368 Do Not Draw Reject  = .05  = 368  X 0

  36. Finding PowerSteps 2 & 3 Reject  n =15/25 Hypothesis:H0: 0 368H1: 0 < 368 Do Not Draw Reject  = .05  = 368  X 0  ‘True’ Situation:1 = 360 Draw   1- Specify  X  = 360 1

  37. Finding PowerStep 4 Reject  n =15/25 Hypothesis:H0: 0 368H1: 0 < 368 Do Not Draw Reject  = .05  = 368  X 0  ‘True’ Situation:1 = 360 Draw   Specify  X  = 360 363.065 1

  38. Finding PowerStep 5 Reject  n =15/25 Hypothesis:H0: 0 368H1: 0 < 368 Do Not Draw Reject  = .05  = 368  X 0  ‘True’ Situation:1 = 360 Draw  = .154    1- =.846 Specify Z Table  X  = 360 363.065 1

  39. Power Curves H0: 0 H0: 0 Power Power Possible True Values for 1 Possible True Values for 1 H0:  =0 Power  = 368 in Example Possible True Values for 1

  40. Conclusion • 1. Distinguished Types of Hypotheses • 2. Described Hypothesis Testing Process • 3. Explained p-Value Concept • 4. Solved Hypothesis Testing Problems Based on a Single Sample • 5. Explained Power of a Test

  41. End of Chapter Any blank slides that follow are blank intentionally.

More Related