1 / 109

Hypothesis Testing

Hypothesis Testing. Learning Objectives. 1. Solve Hypothesis Testing Problems for Two Populations Mean Proportion Variance 2. Distinguish Independent & Related Populations. Who Gets Higher Grades: Males or Females?. Which Programs Are Faster to Learn: Windows or DOS?. Thinking Challenge.

avram-carrillo
Download Presentation

Hypothesis Testing

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. Hypothesis Testing

  2. Learning Objectives 1. Solve Hypothesis Testing Problems for Two Populations • Mean • Proportion • Variance 2. Distinguish Independent & Related Populations

  3. Who Gets Higher Grades: Males or Females? Which Programs Are Faster to Learn: Windows or DOS? Thinking Challenge How Would You Try to Answer These Questions? D O S

  4. Two Population Tests

  5. Testing Two Means Independent Sampling& Paired Difference Experiments

  6. Two Population Tests

  7. Independent & Related Populations Independent Related

  8. 1. Different Data Sources Unrelated Independent Independent & Related Populations Independent Related

  9. 1. Different Data Sources Unrelated Independent 1. Same Data Source Paired or Matched Repeated Measures(Before/After) Independent & Related Populations Independent Related

  10. 1. Different Data Sources Unrelated Independent 2. Use Difference Between the 2 Sample Means X1 -X2 1. Same Data Source Paired or Matched Repeated Measures(Before/After) Independent & Related Populations Independent Related

  11. 1. Different Data Sources Unrelated Independent 2. Use Difference Between the 2 Sample Means X1 -X2 1. Same Data Source Paired or Matched Repeated Measures(Before/After) 2. Use Difference Between Each Pair of Observations Di= X1i - X2i Independent & Related Populations Independent Related

  12. Two Independent Populations Examples 1. An economist wishes to determine whether there is a difference in mean family income for households in 2 socioeconomic groups. 2. An admissions officer of a small liberal arts college wants to compare the scores of applicants educated in rural high schools & in urban high schools.

  13. These are comparative studies. The general purpose of comparative studies is to establish similarities or to detect and measure differences between populations. The populations can be (1) existing populations or (2) hypothetical populations.

  14. Two Related Populations Examples 1. Nike wants to see if there is a difference in durability of 2 sole materials. One type is placed on one shoe, the other type on the other shoe of the same pair. 2. An analyst for Educational Testing Service wants to compare the scores of students before & after taking a review course.

  15. Thinking Challenge Are They Independent or Paired? 1. Miles per gallon ratings of cars before & after mounting radial tires 2. The life expectancy of light bulbs made in 2 different factories 3. Difference in hardness between 2 metals: one contains an alloy, one doesn’t 4. Tread life of two different motorcycle tires: one on the front, the other on the back

  16. Testing 2 Independent Means

  17. Two Population Tests

  18. Two Independent PopulationsHypotheses for Means

  19. Two Independent PopulationsHypotheses for Means

  20. Two Independent PopulationsHypotheses for Means

  21. Sampling Distribution

  22. Sampling Distribution  Population 1 1  1

  23.   2 Sampling Distribution   Population Population 2 1 1 2  1

  24.   2 Sampling Distribution   Population Population 2 1 1 2  1 Select simple random sample, size n . 1 Compute  X 1

  25.   2 Sampling Distribution   Population Population 2 1 1 2  1 Select simple random Select simple random sample, size n . sample, size n . 1 2 Compute  X Compute  X 1 2

  26.   2 Sampling Distribution   Population Population 2 1 1 2  1 Select simple random Compute  X -  X Select simple random 1 2 sample, size n . for every pair sample, size n . 1 2 Compute  X of samples Compute  X 1 2

  27.   2 Sampling Distribution   Population Population 2 1 1 2  1 Select simple random Compute  X -  X Select simple random 1 2 sample, size n . for every pair sample, size n . 1 2 Compute  X of samples Compute  X 1 2 Astronomical number of  X -  X values 1 2

  28. Sampling Distribution

  29. Large-Sample Z Test for 2 Independent Means

  30. Two Population Tests

  31. Large-Sample Z Test for 2 Independent Means

  32. X  X X  X 1 2 1 2   2 2 2 2   s s 1 2 1 2   n n n n 1 2 1 2 Large-Sample Z Test for 2 Independent Means • 1. Assumptions • Independent, Random Samples • Populations Are Normally Distributed • If Not Normal, Can Be Approximated by Normal Distribution (n1 30 & n2 30 ) 2. Two Independent Sample Z-Test Statistic Z

  33. Large-Sample Z Test Example You want to find out if there is a difference in length of long-distance calls between men and women. You collect the following data: WOMENMENNumber 121 125 Mean 3.27 2.53 Std Dev 1.30 1.16 Is there a difference in averagelength ( = 0.05)?

  34. Large-Sample Z Test Solution H0: Ha:  n1 =, n2 = Critical Value(s): Test Statistic: Decision: Conclusion:

  35. Large-Sample Z Test Solution H0: 1 - 2 = 0 (1 = 2) Ha: 1 - 2 0 (1 2)  n1 =, n2 = Critical Value(s): Test Statistic: Decision: Conclusion:

  36. Large-Sample Z Test Solution H0: 1 - 2 = 0 (1 = 2) Ha: 1 - 2 0 (1 2) 0.05 n1 = 121, n2 = 125 Critical Value(s): Test Statistic: Decision: Conclusion:

  37. Large-Sample Z Test Solution H0: 1 - 2 = 0 (1 = 2) Ha: 1 - 2 0 (1 2) 0.05 n1 = 121, n2 = 125 Critical Value(s): Test Statistic: Decision: Conclusion: Reject H Reject H 0 0 0.025 z 0 -1.96 1.96

  38. Large-Sample Z Test Solution H0: 1 - 2 = 0 (1 = 2) Ha: 1 - 2 0 (1 2) 0.05 n1 = 121, n2 = 125 Critical Value(s): Test Statistic: Decision: Conclusion: 3 . 27  2 . 53 z    4 . 69 353 1 . 698 1 .  121 125 Reject H Reject H 0 0 0.025 z 0 -1.96 1.96

  39. Large-Sample Z Test Solution H0: 1 - 2 = 0 (1 = 2) Ha: 1 - 2 0 (1 2) 0.05 n1 = 121, n2 = 125 Critical Value(s): Test Statistic: Decision: Conclusion: 3 . 27  2 . 53 z    4 . 69 1 . 698 1 . 353  121 125 Reject H Reject H Reject at  = 0.05 0 0 0.025 0.025 z 0 -1.96 1.96

  40. Large-Sample Z Test Solution H0: 1 - 2 = 0 (1 = 2) Ha: 1 - 2 0 (1 2) 0.05 n1 = 121, n2 = 125 Critical Value(s): Test Statistic: Decision: Conclusion: 3 . 27  2 . 53 z    4 . 69 1 . 698 1 . 353  121 125 Reject H Reject H Reject at  = 0.05 0 0 0.025 0.025 There is Evidence of a Difference in Means z 0 -1.96 1.96

  41. Large-Sample Z Test Thinking Challenge You’re an economist for the Department of Education. You want to find out if there is a difference in spending per pupil between urban & rural high schools. You collect the following: UrbanRural Number 35 35 Mean $ 6,012 $ 5,832 Std Dev $ 602 $ 497 Is there any difference in population means ( = 0.10)?

  42. Large-Sample Z Test Solution H0: 1 - 2 = 0 (1 = 2) Ha: 1 - 2 0 (1 2) 0.10 n1 = 35, n2 = 35 Critical Value(s): Test Statistic: Decision: Conclusion: 6012  5832 z    1 . 36 2 2 602 497  35 35 Reject H Reject H Do Not Reject at  = 0.10 0 0 0.05 0.05 There is No Evidence of a Difference in Means z 0 -1.645 1.645

  43. Small-Sample t Test for 2 Independent Means

  44. Two Population Tests

  45. Small-Sample t Test for 2 Independent Means 1. Tests Means of 2 Independent Populations Having Equal Variances 2. Assumptions • Independent, Random Samples • Both Populations Are Normally Distributed • Population Variances Are Unknown But Assumed Equal

  46. Small-Sample t Test Test Statistic

  47. Small-Sample t Test Example You want to find out if there is a difference in length of long-distance calls between men and women. You collect the following data: WOMENMENNumber 21 25 Mean 3.27 2.53 Std Dev 1.30 1.16 Is there a difference in averagelength ( = 0.05)?

  48. Small-Sample t Test Solution

  49. Small-Sample t Test Solution Test Statistic: Decision: Conclusion: H0: Ha:  df  Critical Value(s):

  50. Small-Sample t Test Solution Test Statistic: Decision: Conclusion: H0:1 - 2 = 0 (1 = 2) Ha:1 - 2 0 (1 2)  df  Critical Value(s):

More Related