4. 5-1 Introduction

5. 5-2 Inference on the Means of Two Populations, Variances Known Assumptions

6. 5-2 Inference on the Means of Two Populations, Variances Known 5-2.1 Hypothesis Testing on the Difference in Means, Variances Known

7. 5-2 Inference on the Means of Two Populations, Variances Known 5-2.2 Type II Error and Choice of Sample Size

8. 5-2 Inference on the Means of Two Populations, Variances Known 5-2.2 Type II Error and Choice of Sample Size

9. 5-2 Inference on the Means of Two Populations, Variances Known 5-2.3 Confidence Interval on the Difference in Means, Variances Known

10. 5-2 Inference on the Means of Two Populations, Variances Known

11. 5-2 Inference on the Means of Two Populations, Variances Known

12. 5-2 Inference on the Means of Two Populations, Variances Known 5-2.3 Confidence Interval on the Difference in Means, Variances Known Choice of Sample Size

13. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.1 Hypothesis Testing on the Difference in Means

14. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.1 Hypothesis Testing on the Difference in Means

15. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.1 Hypothesis Testing on the Difference in Means

16. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.1 Hypothesis Testing on the Difference in Means

17. 5-3 Inference on the Means of Two Populations, Variances Unknown

18. 5-3 Inference on the Means of Two Populations, Variances Unknown

19. 5-3 Inference on the Means of Two Populations, Variances Unknown

20. 5-3 Inference on the Means of Two Populations, Variances Unknown

21. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.1 Hypothesis Testing on the Difference in Means

22. 5-3 Inference on the Means of Two Populations, Variances Unknown

23. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.2 Type II Error and Choice of Sample Size

24. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.3 Confidence Interval on the Difference in Means

25. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.3 Confidence Interval on the Difference in Means

26. 5-3 Inference on the Means of Two Populations, Variances Unknown 5-3.3 Confidence Interval on the Difference in Means

27. 5-4 The Paired t-Test A special case of the two-sample t-tests of Section 5- 3 occurs when the observations on the two populations of interest are collected in pairs. Each pair of observations, say (X 1j, X 2j ), is taken under homogeneous conditions, but these conditions may change from one pair to another. The test procedure consists of analyzing the differences between hardness readings on each specimen.

28. 5-4 The Paired t-Test

32. Paired Versus Unpaired Comparisons

33. 5-4 The Paired t-Test Confidence Interval for  D

34. 5-4 The Paired t-Test

36. 5-5 Inference on the Ratio of Variances of Two Normal Populations 5-5.1 The F Distribution We wish to test the hypotheses: The development of a test procedure for these hypotheses requires a new probability distribution, the F distribution.

37. 5-5 Inference on the Ratio of Variances of Two Normal Populations 5-5.1 The F Distribution

38. 5-5 Inference on the Ratio of Variances of Two Normal Populations 5-5.1 The F Distribution

39. 5-5 Inference on the Ratio of Variances of Two Normal Populations The Test Procedure

40. 5-5 Inference on the Ratio of Variances of Two Normal Populations The Test Procedure

41. 5-5 Inference on the Ratio of Variances of Two Normal Populations The Test Procedure

42. 5-5 Inference on the Ratio of Variances of Two Normal Populations 5-5.2 Confidence Interval on the Ratio of Two Variances

43. 5-5 Inference on the Ratio of Variances of Two Normal Populations

44. 5-5 Inference on the Ratio of Variances of Two Normal Populations

45. 5-6 Inference on Two Population Proportions 5-6.1 Hypothesis Testing on the Equality of Two Binomial Proportions

46. 5-6 Inference on Two Population Proportions 5-6.1 Hypothesis Testing on the Equality of Two Binomial Proportions

47. 5-6 Inference on Two Population Proportions

48. 5-6 Inference on Two Population Proportions

49. 5-6 Inference on Two Population Proportions

50. 5-6 Inference on Two Population Proportions 5-6.2 Type II Error and Choice of Sample Size

51. 5-6 Inference on Two Population Proportions 5-6.2 Type II Error and Choice of Sample Size

52. 5-6 Inference on Two Population Proportions 5-6.2 Type II Error and Choice of Sample Size

53. 5-6 Inference on Two Population Proportions 5-6.3 Confidence Interval on the Difference in Binomial Proportions

54. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

55. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance The levels of the factor are sometimes called treatments. Each treatment has six observations or replicates. The runs are run in random order.

56. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

57. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

58. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

59. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

60. 5-8 What If We Have More Than Two Samples?

61. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

62. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

63. 5-8 What If We Have More Than Two Samples?

64. 5-8 What If We Have More Than Two Samples? 5-8.1 Completely Randomized Experiment and Analysis of Variance

65. 5-8 What If We Have More Than Two Samples? Which means differ?

66. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking

67. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking

68. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking

69. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking

70. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment The randomized block design is an extension of the paired t-test to situations where the factor of interest has more than two levels.

71. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment For example, consider the situation where two different methods were used to predict the shear strength of steel plate girders. Say we use four girders as the experimental units.

72. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment

73. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment The appropriate linear statistical model: We assume treatments and blocks are initially fixed effects blocks do not interact

74. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment The hypotheses of interest are:

75. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment

76. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment The mean squares are:

77. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment The expected values of these mean squares are:

78. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment

79. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment

80. 5-8 What If We Have More Than Two Samples?

81. 5-8 What If We Have More Than Two Samples?

82. 5-8 What If We Have More Than Two Samples?

83. 5-8 What If We Have More Than Two Samples?

84. 5-8 What If We Have More Than Two Samples? Which means differ?

85. 5-8 What If We Have More Than Two Samples? 5-8.2 Randomized Complete Block Experiment

86. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking

87. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking

88. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking

89. 5-8 What If We Have More Than Two Samples? Residual Analysis and Model Checking