4. 10-1 Introduction

5. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Figure 10-1 Two independent populations.

6. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Assumptions

7. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known

8. 10-2.1 Hypothesis Tests for a Difference in Means, Variances Known

9. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Example 10-1

10. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Example 10-1

11. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Example 10-1

12. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known 10-2.2 Type II Error and Choice of Sample Size Use of Operating Characteristic Curves Two-sided alternative: One-sided alternative:

13. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known 10-2.2 Type II Error and Choice of Sample Size Sample Size Formulas Two-sided alternative:

14. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known 10-2.2 Type II Error and Choice of Sample Size Sample Size Formulas One-sided alternative:

15. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Example 10-3

16. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known 10-2.3 Confidence Interval on a Difference in Means, Variances Known Definition

17. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Example 10-4

18. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Example 10-4

19. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Choice of Sample Size

20. 10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known One-Sided Confidence Bounds Upper Confidence Bound Lower Confidence Bound

21. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown We wish to test: Case 1:

22. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown The pooled estimator of  2 : Case 1:

23. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown Case 1:

24. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Definition: The Two-Sample or Pooled t-Test *

25. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-5

26. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-5

27. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-5

28. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-5

29. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Minitab Output for Example 10-5

30. Figure 10-2 Normal probability plot and comparative box plot for the catalyst yield data in Example 10-5. (a) Normal probability plot, (b) Box plots. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown

31. 10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown Case 2: is distributed approximately as t with degrees of freedom given by

32. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown Case 2:

33. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-6

34. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-6 (Continued)

35. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-6 (Continued)

36. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-6 (Continued) Figure 10-3 Normal probability plot of the arsenic concentration data from Example 10-6.

37. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-6 (Continued)

38. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 10-3.2 Type II Error and Choice of Sample Size Example 10-7

39. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Minitab Output for Example 10-7

40. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 10-3.3 Confidence Interval on the Difference in Means, Variance Unknown Case 1:

41. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-8 Case 1:

42. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Case 1: Example 10-8 (Continued)

43. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Case 1: Example 10-8 (Continued)

44. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown Example 10-8 (Continued) Case 1:

45. 10-3 Inference for a Difference in Means of Two Normal Distributions, Variances Unknown 10-3.3 Confidence Interval on the Difference in Means, Variance Unknown Case 2:

46. A special case of the two-sample t-tests of Section 10-3 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. 10-4 Paired t-Test

47. The Paired t-Test 10-4 Paired t-Test

48. Example 10-9 10-4 Paired t-Test

49. Example 10-9 10-4 Paired t-Test

50. Example 10-9 10-4 Paired t-Test

51. Paired Versus Unpaired Comparisons 10-4 Paired t-Test

52. A Confidence Interval for  D 10-4 Paired t-Test Definition

53. Example 10-10 10-4 Paired t-Test

54. Example 10-10 10-4 Paired t-Test

55. 10-5.1 The F Distribution 10-5 Inferences on the Variances of Two Normal Populations We wish to test the hypotheses: The development of a test procedure for these hypotheses requires a new probability distribution, the F distribution.

56. 10-5.1 The F Distribution 10-5 Inferences on the Variances of Two Normal Populations

57. 10-5.1 The F Distribution 10-5 Inferences on the Variances of Two Normal Populations

58. 10-5.1 The F Distribution 10-5 Inferences on the Variances of Two Normal Populations The lower-tail percentage points f  -1,u, can be found as follows.

59. 10-5.2 Hypothesis Tests on the Ratio of Two Variances 10-5 Inferences on the Variances of Two Normal Populations

60. 10-5.2 Hypothesis Tests on the Ratio of Two Variances 10-5 Inferences on the Variances of Two Normal Populations

61. Example 10-11 10-5 Inferences on the Variances of Two Normal Populations

62. Example 10-11 10-5 Inferences on the Variances of Two Normal Populations

63. Example 10-11 10-5 Inferences on the Variances of Two Normal Populations

64. 10-5.3 Type II Error and Choice of Sample Size 10-5 Inferences on the Variances of Two Normal Populations

65. Example 10-12 10-5 Inferences on the Variances of Two Normal Populations

66. 10-5.4 Confidence Interval on the Ratio of Two Variances 10-5 Inferences on the Variances of Two Normal Populations

67. Example 10-13 10-5 Inferences on the Variances of Two Normal Populations

68. Example 10-13 10-5 Inferences on the Variances of Two Normal Populations

69. Example 10-13 10-5 Inferences on the Variances of Two Normal Populations

70. 10-6.1 Large-Sample Test on the Difference in Population Proportions 10-6 Inference on Two Population Proportions We wish to test the hypotheses :

71. 10-6.1 Large-Sample Test on the Difference in Population Proportions 10-6 Inference on Two Population Proportions The following test statistic is distributed approximately as standard normal and is the basis of the test :

72. 10-6 Inference on Two Population Proportions 10-6.1 Large-Sample Test on the Difference in Population Proportions

73. Example 10-14 10-6 Inference on Two Population Proportions

74. Example 10-14 10-6 Inference on Two Population Proportions

75. Example 10-14 10-6 Inference on Two Population Proportions

76. Minitab Output for Example 10-14 10-6 Inference on Two Population Proportions

77. 10-6.2 Type II Error and Choice of Sample Size 10-6 Inference on Two Population Proportions

78. 10-6.2 Type II Error and Choice of Sample Size 10-6 Inference on Two Population Proportions

79. 10-6.2 Type II Error and Choice of Sample Size 10-6 Inference on Two Population Proportions

80. 10-6.3 Confidence Interval on the Difference in the Population Proportions 10-6 Inference on Two Population Proportions

81. Example 10-15 10-6 Inference on Two Population Proportions

82. Example 10-15 10-6 Inference on Two Population Proportions

83. 10-7 Summary Table and Road Map for Inference Procedures for Two Samples Table 10-4

84. 10-7 Summary Table and Road Map for Inference Procedures for Two Samples Table 10-4 (Continued)