1. 8 - 1 © 1998 Prentice-Hall, Inc. Chapter 8 Inferences Based on a Single Sample: Tests of Hypothesis

2. 8 - 2 © 1998 Prentice-Hall, Inc. Learning Objectives 1.Distinguish types of hypotheses 2.Describe hypothesis testing process 3.Explain p-value concept 4.Solve hypothesis testing problems based on a single sample

3. 8 - 3 © 1998 Prentice-Hall, Inc. Types of Statistical Applications

4. 8 - 4 © 1998 Prentice-Hall, Inc. Hypothesis Testing Concepts

5. 8 - 5 © 1998 Prentice-Hall, Inc. Hypothesis Testing

6. 8 - 6 © 1998 Prentice-Hall, Inc. Hypothesis Testing Population

7. 8 - 7 © 1998 Prentice-Hall, Inc. Hypothesis Testing Population I believe the population mean age is 50 (hypothesis).

8. 8 - 8 © 1998 Prentice-Hall, Inc. Hypothesis Testing Population I believe the population mean age is 50 (hypothesis). Mean  X = 20 Random sample

9. 8 - 9 © 1998 Prentice-Hall, Inc. Hypothesis Testing Population I believe the population mean age is 50 (hypothesis). Mean  X = 20 Reject hypothesis! Not close. Random sample

10. 8 - 10 © 1998 Prentice-Hall, Inc. What’s a Hypothesis? 1.A belief about a population parameter Parameter is population mean, proportion, variance Parameter is population mean, proportion, variance Must be stated before analysis Must be stated before analysis

11. 8 - 11 © 1998 Prentice-Hall, Inc. What’s a Hypothesis? 1.A belief about a population parameter Parameter is population mean, proportion, variance Parameter is population mean, proportion, variance Must be stated before analysis Must be stated before analysis I believe the mean GPA of this class is 3.5! © 1984-1994 T/Maker Co.

12. 8 - 12 © 1998 Prentice-Hall, Inc. Null Hypothesis 1.What is tested 2.Has serious outcome if incorrect decision made 3.Always has equality sign: , or  4.Designated H 0 5.Specified as H 0 :   Some numeric value Written with = sign even if , or  Written with = sign even if , or  Example, H 0 :   3 Example, H 0 :   3

13. 8 - 13 © 1998 Prentice-Hall, Inc. Alternative Hypothesis 1.Opposite of null hypothesis 2.Always has inequality sign: , , or  3.Designated H a 4.Specified H a :  < Some value Example, H a :  < 3 Example, H a :  < 3

14. 8 - 14 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps

15. 8 - 15 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically

16. 8 - 16 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically Example Is the population mean different from 3?

17. 8 - 17 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically Example Is the population mean different from 3? 1.   3

18. 8 - 18 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustiveExample Is the population mean different from 3? 1.   3

19. 8 - 19 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustiveExample Is the population mean different from 3? 1.   3 2.  = 3

20. 8 - 20 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , signExample Is the population mean different from 3? 1.   3 2.  = 3

21. 8 - 21 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , signExample Is the population mean different from 3? 1.   3 2.  = 3 3. H a :   3

22. 8 - 22 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population mean different from 3? 1.   3 2.  = 3 3. H a :   3

23. 8 - 23 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Steps Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population mean different from 3? 1.   3 2.  = 3 3. H a :   3 4. H 0 :  = 3

24. 8 - 24 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 1 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing 12 hours? 1.2.3.4.

25. 8 - 25 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 1 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing 12 hours? 1.  = 12 2.3.4.

26. 8 - 26 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 1 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing 12 hours? 1.  = 12 2.   12 3.4.

27. 8 - 27 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 1 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing 12 hours? 1.  = 12 2.   12 3. H a :   12 4.

28. 8 - 28 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 1 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing 12 hours? 1.  = 12 2.   12 3. H a :   12 4. H 0 :  = 12

29. 8 - 29 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 2 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing different from 12 hours? 1.2.3.4.

30. 8 - 30 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 2 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing different from 12 hours? 1.   12 2.3.4.

31. 8 - 31 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 2 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing different from 12 hours? 1.   12 2.  = 12 3.4.

32. 8 - 32 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 2 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing different from 12 hours? 1.   12 2.  = 12 3. H a :   12 4.

33. 8 - 33 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 2 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the population average amount of TV viewing different from 12 hours? 1.   12 2.  = 12 3. H a :   12 4. H 0 :  = 12

34. 8 - 34 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 3 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average cost per hat less than or equal to $20? 1.2.3.4.

35. 8 - 35 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 3 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average cost per hat less than or equal to $20? 1.   20 2.3.4.

36. 8 - 36 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 3 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average cost per hat less than or equal to $20? 1.   20 2.  20 3.4.

37. 8 - 37 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 3 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average cost per hat less than or equal to $20? 1.   20 2.  20 3. H a :   20 4.

38. 8 - 38 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 3 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average cost per hat less than or equal to $20? 1.   20 2.  20 3. H a :   20 4. H 0 :  = 20

39. 8 - 39 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 4 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average amount spent in the bookstore greater than $25? 1.2.3.4.

40. 8 - 40 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 4 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average amount spent in the bookstore greater than $25? 1.   25 2.3.4.

41. 8 - 41 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 4 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average amount spent in the bookstore greater than $25? 1.   25 2.  25 3.4.

42. 8 - 42 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 4 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average amount spent in the bookstore greater than $25? 1.   25 2.  25 3. H a :   25 4.

43. 8 - 43 © 1998 Prentice-Hall, Inc. Identifying Hypotheses Example 4 Steps 1.State question statistically 2.State opposite statistically Must be mutually exclusive & exhaustive Must be mutually exclusive & exhaustive 3.Select & state alternative hypothesis Has the , sign Has the , sign 4.State null hypothesis Example Is the average amount spent in the bookstore greater than $25? 1.   25 2.  25 3. H a :   25 4. H 0 :  = 25

44. 8 - 44 © 1998 Prentice-Hall, Inc. Basic Idea

45. 8 - 45 © 1998 Prentice-Hall, Inc. Basic Idea H0H0H0H0 H0H0H0H0 Sampling Distribution

46. 8 - 46 © 1998 Prentice-Hall, Inc. Basic Idea Sampling Distribution It is unlikely that we would get a sample mean of this value... 2020 H0H0H0H0 H0H0H0H0

47. 8 - 47 © 1998 Prentice-Hall, Inc. Basic Idea Sampling Distribution It is unlikely that we would get a sample mean of this value...... if in fact this were the population mean 2020 H0H0H0H0 H0H0H0H0

48. 8 - 48 © 1998 Prentice-Hall, Inc. Basic Idea Sampling Distribution It is unlikely that we would get a sample mean of this value...... if in fact this were the population mean... therefore, we reject the hypothesis that  = 50. 2020 H0H0H0H0 H0H0H0H0

49. 8 - 49 © 1998 Prentice-Hall, Inc. Level of Significance 1.Defines unlikely values of sample statistic if null hypothesis is true Called rejection region of sampling distribution Called rejection region of sampling distribution 2.Is a probability 3.Denoted  (alpha) 4.Selected by researcher at start Typical values are.01,.05,.10 Typical values are.01,.05,.10

50. 8 - 50 © 1998 Prentice-Hall, Inc. Rejection Region (One-Tail Test)

51. 8 - 51 © 1998 Prentice-Hall, Inc. Ho Value Sample Statistic Rejection Region (One-Tail Test) Sampling Distribution

52. 8 - 52 © 1998 Prentice-Hall, Inc. Ho Value Sample Statistic Rejection Region Rejection Region (One-Tail Test) Sampling Distribution

53. 8 - 53 © 1998 Prentice-Hall, Inc. Ho Value Sample Statistic Rejection Region Nonrejection Region Rejection Region (One-Tail Test) Sampling Distribution

54. 8 - 54 © 1998 Prentice-Hall, Inc. Ho Value Sample Statistic Rejection Region Nonrejection Region Rejection Region (One-Tail Test) Sampling Distribution Critical Value

55. 8 - 55 © 1998 Prentice-Hall, Inc. Ho Value   Sample Statistic Rejection Region Nonrejection Region Rejection Region (One-Tail Test) Sampling Distribution Critical Value

56. 8 - 56 © 1998 Prentice-Hall, Inc. Rejection Region (One-Tail Test) Sampling Distribution 1 -  Level of Confidence

57. 8 - 57 © 1998 Prentice-Hall, Inc. Rejection Region (One-Tail Test) Sampling Distribution 1 -  Level of Confidence Observed sample statistic

58. 8 - 58 © 1998 Prentice-Hall, Inc. Rejection Region (One-Tail Test) Sampling Distribution 1 -  Level of Confidence

59. 8 - 59 © 1998 Prentice-Hall, Inc. Rejection Regions (Two-Tailed Test)

60. 8 - 60 © 1998 Prentice-Hall, Inc. Ho Value Sample Statistic Rejection Regions (Two-Tailed Test) Sampling Distribution

61. 8 - 61 © 1998 Prentice-Hall, Inc. Ho Value Sample Statistic Rejection Region Rejection Region Rejection Regions (Two-Tailed Test) Sampling Distribution

62. 8 - 62 © 1998 Prentice-Hall, Inc. Ho Value Sample Statistic Rejection Region Rejection Region Nonrejection Region Rejection Regions (Two-Tailed Test) Sampling Distribution

63. 8 - 63 © 1998 Prentice-Hall, Inc. Ho Value Critical Value Critical Value Sample Statistic Rejection Region Rejection Region Nonrejection Region Rejection Regions (Two-Tailed Test) Sampling Distribution

64. 8 - 64 © 1998 Prentice-Hall, Inc. Ho Value Critical Value Critical Value 1/2     Sample Statistic Rejection Region Rejection Region Nonrejection Region Rejection Regions (Two-Tailed Test) Sampling Distribution

65. 8 - 65 © 1998 Prentice-Hall, Inc. Rejection Regions (Two-Tailed Test) Sampling Distribution 1 -  Level of Confidence

66. 8 - 66 © 1998 Prentice-Hall, Inc. Rejection Regions (Two-Tailed Test) Sampling Distribution 1 -  Level of Confidence

67. 8 - 67 © 1998 Prentice-Hall, Inc. Rejection Regions (Two-Tailed Test) Sampling Distribution 1 -  Level of Confidence

68. 8 - 68 © 1998 Prentice-Hall, Inc. Rejection Regions (Two-Tailed Test) Sampling Distribution 1 -  Level of Confidence

69. 8 - 69 © 1998 Prentice-Hall, Inc. Decision Making Risks

70. 8 - 70 © 1998 Prentice-Hall, Inc. Errors in Making Decision 1.Type I error Reject true null hypothesis Reject true null hypothesis Has serious consequences Has serious consequences Probability of Type I error is  (alpha) Probability of Type I error is  (alpha) Called level of significance Called level of significance 2.Type II error Do not reject false null hypothesis Do not reject false null hypothesis Probability of Type II error is  (beta) Probability of Type II error is  (beta)

71. 8 - 71 © 1998 Prentice-Hall, Inc. Decision Results H 0 : Innocent

72. 8 - 72 © 1998 Prentice-Hall, Inc. Decision Results H 0 : Innocent

73. 8 - 73 © 1998 Prentice-Hall, Inc. Hypothesis Testing Steps

74. 8 - 74 © 1998 Prentice-Hall, Inc. H 0 Testing Steps

75. 8 - 75 © 1998 Prentice-Hall, Inc. H 0 Testing Steps n State H 0 n State H 1 Choose  Choose  n Choose n n Choose test

76. 8 - 76 © 1998 Prentice-Hall, Inc. H 0 Testing Steps n Set up critical values n Collect data n Compute test statistic n Make statistical decision n Express decision n State H 0 n State H 1 Choose  Choose  n Choose n n Choose test

77. 8 - 77 © 1998 Prentice-Hall, Inc. One Population Tests

78. 8 - 78 © 1998 Prentice-Hall, Inc. One Population Tests One Population

79. 8 - 79 © 1998 Prentice-Hall, Inc. One Population Tests One Population Mean

80. 8 - 80 © 1998 Prentice-Hall, Inc. One Population Tests One Population MeanProportion

81. 8 - 81 © 1998 Prentice-Hall, Inc. One Population Tests One Population Z Test (1 & 2 tail) MeanProportion LargeLarge SampleSample

82. 8 - 82 © 1998 Prentice-Hall, Inc. One Population Tests One Population Z Test (1 & 2 tail) t Test (1 & 2 tail) MeanProportion LargeLarge SampleSample SmallSmall SampleSample

83. 8 - 83 © 1998 Prentice-Hall, Inc. One Population Tests

84. 8 - 84 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test of Mean (Large Sample)

85. 8 - 85 © 1998 Prentice-Hall, Inc. One Population Tests

86. 8 - 86 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test for Mean (Large Sample) 1.Assumptions Sample size at least 30 (n  30) Sample size at least 30 (n  30) If population standard deviation unknown, use sample standard deviation If population standard deviation unknown, use sample standard deviation 2.Alternative hypothesis has  sign

87. 8 - 87 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test for Mean (Large Sample) 1.Assumptions Sample size at least 30 (n  30) Sample size at least 30 (n  30) If population standard deviation unknown, use sample standard deviation If population standard deviation unknown, use sample standard deviation 2.Alternative hypothesis has  sign 3.Z-test statistic

88. 8 - 88 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Example Does an average box of cereal contain 368 grams of cereal? A random sample of 36 boxes showed  X = 372.5. The company has specified  to be 25 grams. Test at the.05 level. 368 gm.

89. 8 - 89 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution H 0 : H a :   n  Critical Value(s): Test Statistic: Decision:Conclusion:

90. 8 - 90 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution H 0 :  = 368 H a :   368   n  Critical Value(s): Test Statistic: Decision:Conclusion:

91. 8 - 91 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution H 0 :  = 368 H a :   368  .05 n  36 Critical Value(s): Test Statistic: Decision:Conclusion:

92. 8 - 92 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution H 0 :  = 368 H a :   368  .05 n  36 Critical Value(s): Test Statistic: Decision:Conclusion:

93. 8 - 93 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution H 0 :  = 368 H a :   368  .05 n  36 Critical Value(s): Test Statistic: Decision:Conclusion:

94. 8 - 94 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution H 0 :  = 368 H a :   368  .05 n  36 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05

95. 8 - 95 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution H 0 :  = 368 H a :   368  .05 n  36 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05 No evidence average is not 368

96. 8 - 96 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Thinking Challenge You’re a Q/C inspector. You want to find out if a new machine is making electrical cords to customer specification: average breaking strength of 70 lb. with  = 3.5 lb. You take a sample of 36 cords & compute a sample mean of 69.7 lb. At the.05 level, is there evidence that the machine is not meeting the average breaking strength? AloneGroupClass

97. 8 - 97 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution* H 0 : H a :  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

98. 8 - 98 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution* H 0 :  = 70 H a :   70  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

99. 8 - 99 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution* H 0 :  = 70 H a :   70  =.05 n = 36 Critical Value(s): Test Statistic: Decision:Conclusion:

100. 8 - 100 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution* H 0 :  = 70 H a :   70  =.05 n = 36 Critical Value(s): Test Statistic: Decision:Conclusion:

101. 8 - 101 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution* H 0 :  = 70 H a :   70  =.05 n = 36 Critical Value(s): Test Statistic: Decision:Conclusion:

102. 8 - 102 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution* H 0 :  = 70 H a :   70  =.05 n = 36 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05

103. 8 - 103 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test Solution* H 0 :  = 70 H a :   70  =.05 n = 36 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05 No evidence average is not 70

104. 8 - 104 © 1998 Prentice-Hall, Inc. One-Tailed Z Test of Mean (Large Sample)

105. 8 - 105 © 1998 Prentice-Hall, Inc. One-Tailed Z Test for Mean (Large Sample) 1.Assumptions Sample size at least 30 (n  30) Sample size at least 30 (n  30) If population standard deviation unknown, use sample standard deviation If population standard deviation unknown, use sample standard deviation 2.Alternative hypothesis has sign

106. 8 - 106 © 1998 Prentice-Hall, Inc. One-Tailed Z Test for Mean (Large Sample) 1.Assumptions Sample size at least 30 (n  30) Sample size at least 30 (n  30) If population standard deviation unknown, use sample standard deviation If population standard deviation unknown, use sample standard deviation 2.Alternative hypothesis has  or > sign 3.Z-test statistic

107. 8 - 107 © 1998 Prentice-Hall, Inc. One-Tailed Z Test for Mean Hypotheses

108. 8 - 108 © 1998 Prentice-Hall, Inc. One-Tailed Z Test for Mean Hypotheses H 0 :  =  0 H a :  < 0 Must be significantly below 

109. 8 - 109 © 1998 Prentice-Hall, Inc. One-Tailed Z Test for Mean Hypotheses H 0 :  =  0 H a :  < 0 H 0 :  =  0 H a :  > 0 Must be significantly below  Small values satisfy H 0. Don’t reject!

110. 8 - 110 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Finding Critical Z

111. 8 - 111 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Finding Critical Z What is Z given  =.025?  =.025 

112. 8 - 112 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Finding Critical Z.500 -.025.475 What is Z given  =.025?  =.025  

113. 8 - 113 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Finding Critical Z.500 -.025.475.06 1.9.4750 Standardized Normal Probability Table (Portion) What is Z given  =.025?  =.025  

114. 8 - 114 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Finding Critical Z.500 -.025.475.06 1.9.4750 Standardized Normal Probability Table (Portion) What is Z given  =.025?  =.025   

115. 8 - 115 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Example Does an average box of cereal contain more than 368 grams of cereal? A random sample of 36 boxes showed  X = 372.5. The company has specified  to be 25 grams. Test at the.05 level. 368 gm.

116. 8 - 116 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution H 0 : H a :  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

117. 8 - 117 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution H 0 :  = 368 H a :  > 368  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

118. 8 - 118 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution H 0 :  = 368 H a :  > 368  =.05 n = 36 Critical Value(s): Test Statistic: Decision:Conclusion:

119. 8 - 119 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution H 0 :  = 368 H a :  > 368  =.05 n = 36 Critical Value(s): Test Statistic: Decision:Conclusion:

120. 8 - 120 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution H 0 :  = 368 H a :  > 368  =.05 n = 25 Critical Value(s): Test Statistic: Decision:Conclusion:

121. 8 - 121 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution H 0 :  = 368 H a :  > 368  =.05 n = 25 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05

122. 8 - 122 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution H 0 :  = 368 H a :  > 368  =.05 n = 25 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05 Evidence average is more than 368

123. 8 - 123 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Thinking Challenge You’re an analyst for Ford. You want to find out if the average miles per gallon of Escorts is at least 32 mpg. Similar models have a standard deviation of 3.8 mpg. You take a sample of 60 Escorts & compute a sample mean of 30.7 mpg. At the.01 level, is there evidence that the miles per gallon is at least 32? AloneGroupClass

124. 8 - 124 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution* H 0 : H a :  = n = Critical Value(s): Test Statistic: Decision:Conclusion: Decision:Conclusion:

125. 8 - 125 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution* H 0 :  = 32 H a :  < 32  = n = Critical Value(s): Test Statistic: Decision:Conclusion: Decision:Conclusion:

126. 8 - 126 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution* H 0 :  = 32 H a :  < 32  =.01 n = 60 Critical Value(s): Test Statistic: Decision:Conclusion: Decision:Conclusion:

127. 8 - 127 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution* H 0 :  = 32 H a :  < 32  =.01 n = 60 Critical Value(s): Test Statistic: Decision:Conclusion: Decision:Conclusion:

128. 8 - 128 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution* H 0 :  = 32 H a :  < 32  =.01 n = 60 Critical Value(s): Test Statistic: Decision:Conclusion: Decision:Conclusion:

129. 8 - 129 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution* H 0 :  = 32 H a :  < 32  =.01 n = 60 Critical Value(s): Test Statistic: Decision:Conclusion: Decision:Conclusion: Reject at  =.01

130. 8 - 130 © 1998 Prentice-Hall, Inc. One-Tailed Z Test Solution* H 0 :  = 32 H a :  < 32  =.01 n = 60 Critical Value(s): Test Statistic: Decision:Conclusion: Decision:Conclusion: Reject at  =.01 There is evidence average is less than 32

131. 8 - 131 © 1998 Prentice-Hall, Inc. Observed Significance Levels: p -Values

132. 8 - 132 © 1998 Prentice-Hall, Inc. p -Value 1.Probability of obtaining a test statistic more extreme (  or  than the actual sample value given H 0 is true 2.Called observed level of significance Smallest value of  H 0 can be rejected Smallest value of  H 0 can be rejected 3.Used to make rejection decision If p-value  , do not reject H 0 If p-value  , do not reject H 0 If p-value < , reject H 0 If p-value < , reject H 0

133. 8 - 133 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Example Does an average box of cereal contain 368 grams of cereal? A random sample of 36 boxes showed  X = 372.5. The company has specified  to be 25 grams. Find the p-value. 368 gm.

134. 8 - 134 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution

135. 8 - 135 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution Z value of sample statistic (observed) 

136. 8 - 136 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution Z value of sample statistic (observed)  p-value = P(Z  -1.80 or Z  1.80)

137. 8 - 137 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution Z value of sample statistic (observed)  p-value = P(Z  -1.80 or Z  1.80)

138. 8 - 138 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution Z value of sample statistic (observed) From Z table: lookup 1.80.4641  p-value = P(Z  -1.80 or Z  1.80)

139. 8 - 139 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution Z value of sample statistic (observed) From Z table: lookup 1.80.4641 .5000 -.4641.0359  p-value = P(Z  -1.80 or Z  1.80)

140. 8 - 140 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution p-value = P(Z  -1.80 or Z  1.80) =.0718 Z value of sample statistic From Z table: lookup 1.80.4641.5000 -.4641.0359  

141. 8 - 141 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution 1/2 p-value =.0359 1/2  =.025

142. 8 - 142 © 1998 Prentice-Hall, Inc. Two-Tailed Z Test p -Value Solution 1/2 p-value =.0359 1/2  =.025 (p-value =.0718)  (  =.05). Do not reject.

143. 8 - 143 © 1998 Prentice-Hall, Inc. One-Tailed Z Test p -Value Example Does an average box of cereal contain more than 368 grams of cereal? A random sample of 36 boxes showed  X = 372.5. The company has specified  to be 25 grams. Find the p-value. 368 gm.

144. 8 - 144 © 1998 Prentice-Hall, Inc. One-Tailed Z Test p -Value Solution

145. 8 - 145 © 1998 Prentice-Hall, Inc. One-Tailed Z Test p -Value Solution Z Z 0 0

146. 8 - 146 © 1998 Prentice-Hall, Inc. One-Tailed Z Test p -Value Solution Use alternative hypothesis to find direction Z Z 0 0 p-value 

147. 8 - 147 © 1998 Prentice-Hall, Inc.   One-Tailed Z Test p -Value Solution Use alternative hypothesis to find direction Z value of sample statistic 1.80

148. 8 - 148 © 1998 Prentice-Hall, Inc.   One-Tailed Z Test p -Value Solution Use alternative hypothesis to find direction Z value of sample statistic p-value is P(Z  1.80)

149. 8 - 149 © 1998 Prentice-Hall, Inc. One-Tailed Z Test p -Value Solution Use alternative hypothesis to find direction p-value is P(Z  1.80) Z value of sample statistic From Z table: lookup 1.80.4641   

150. 8 - 150 © 1998 Prentice-Hall, Inc..4641 One-Tailed Z Test p -Value Solution Use alternative hypothesis to find direction p-value is P(Z  1.80) Z value of sample statistic From Z table: lookup 1.80 .5000 -.4641.0359   

151. 8 - 151 © 1998 Prentice-Hall, Inc..4641 One-Tailed Z Test p -Value Solution Z value of sample statistic From Z table: lookup 1.80 Use alternative hypothesis to find direction.5000 -.4641.0359   p-value is P(Z  1.80) =.0359  

152. 8 - 152 © 1998 Prentice-Hall, Inc. Z Z 0 0 1.80 p-value One-Tailed Z Test p -Value Solution =.0359 =.0359

153. 8 - 153 © 1998 Prentice-Hall, Inc. Z Z 0 0 1.80 p-value One-Tailed Z Test p -Value Solution =.0359 =.0359 Reject  =.05

154. 8 - 154 © 1998 Prentice-Hall, Inc. Z Z 0 0 1.80 p-value One-Tailed Z Test p -Value Solution =.0359 =.0359 Reject  =.05

155. 8 - 155 © 1998 Prentice-Hall, Inc. (p-value =.0359)  (  =.05). Reject. One-Tailed Z Test p -Value Solution =.0359 =.0359 Reject  =.05

156. 8 - 156 © 1998 Prentice-Hall, Inc. p -Value Thinking Challenge You’re an analyst for Ford. You want to find out if the average miles per gallon of Escorts is at least 32 mpg. Similar models have a standard deviation of 3.8 mpg. You take a sample of 60 Escorts & compute a sample mean of 30.7 mpg. What is the value of the observed level of significance (p-value)? AloneGroupClass

157. 8 - 157 © 1998 Prentice-Hall, Inc. p -Value Solution* Z Z 0 0

158. 8 - 158 © 1998 Prentice-Hall, Inc. p -Value Solution* Use alternative hypothesis to find direction 

159. 8 - 159 © 1998 Prentice-Hall, Inc. p -Value Solution* Z value of sample statistic Use alternative hypothesis to find direction  

160. 8 - 160 © 1998 Prentice-Hall, Inc. p -Value Solution* Z value of sample statistic From Z table: lookup 2.65.4960 Use alternative hypothesis to find direction  

161. 8 - 161 © 1998 Prentice-Hall, Inc. p -Value Solution* Z value of sample statistic From Z table: lookup 2.65.4960 Use alternative hypothesis to find direction.5000 -.4960.0040   

162. 8 - 162 © 1998 Prentice-Hall, Inc. p -Value Solution* Z value of sample statistic From Z table: lookup 2.65.4960 Use alternative hypothesis to find direction.5000 -.4960.0040    p-value = P(Z  -2.65) =.004. p-value < (  =.01). Reject H 0.

163. 8 - 163 © 1998 Prentice-Hall, Inc. Two-Tailed t Test of Mean (Small Sample)

164. 8 - 164 © 1998 Prentice-Hall, Inc. One Population Tests

165. 8 - 165 © 1998 Prentice-Hall, Inc. t Test for Mean (Small Sample) 1.Assumptions Sample size is less than 30 (n < 30) Sample size is less than 30 (n < 30) Population is normally distributed Population is normally distributed Population standard deviation is unknown Population standard deviation is unknown

166. 8 - 166 © 1998 Prentice-Hall, Inc. t Test for Mean (Small Sample) 1.Assumptions Sample size is less than 30 (n < 30) Sample size is less than 30 (n < 30) Population is normally distributed Population is normally distributed Population standard deviation is unknown Population standard deviation is unknown 3.T test statistic

167. 8 - 167 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Finding Critical t Values

168. 8 - 168 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Finding Critical t Values Given: n = 3;  =.10

169. 8 - 169 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Finding Critical t Values  /2 =.05  Given: n = 3;  =.10

170. 8 - 170 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Finding Critical t Values  /2 =.05   Given: n = 3;  =.10 df = n - 1 = 2

171. 8 - 171 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Finding Critical t Values Critical Values of t Table (Portion)  /2 =.05    Given: n = 3;  =.10 df = n - 1 = 2

172. 8 - 172 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Finding Critical t Values Critical Values of t Table (Portion)  /2 =.05     Given: n = 3;  =.10 df = n - 1 = 2

173. 8 - 173 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Example Does an average box of cereal contain 368 grams of cereal? A random sample of 25 boxes had a mean of 372.5 & a standard deviation of 12 grams. Test at the.05 level. 368 gm.

174. 8 - 174 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution H 0 : H a :  = df = Critical Value(s): Test Statistic: Decision:Conclusion:

175. 8 - 175 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution H 0 :  = 368 H a :   368  = df = Critical Value(s): Test Statistic: Decision:Conclusion:

176. 8 - 176 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution H 0 :  = 368 H a :   368  =.05 df = 25 - 1 = 24 Critical Value(s): Test Statistic: Decision:Conclusion:

177. 8 - 177 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution H 0 :  = 368 H a :   368  =.05 df = 25 - 1 = 24 Critical Value(s): Test Statistic: Decision:Conclusion:

178. 8 - 178 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution H 0 :  = 368 H a :   368  =.05 df = 25 - 1 = 24 Critical Value(s): Test Statistic: Decision:Conclusion:

179. 8 - 179 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution H 0 :  = 368 H a :   368  =.05 df = 25 - 1 = 24 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05

180. 8 - 180 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution H 0 :  = 368 H a :   368  =.05 df = 25 - 1 = 24 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05 There is no evidence pop. average is not 368

181. 8 - 181 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Thinking Challenge You work for the FTC. A manufacturer of detergent claims that the mean weight of detergent is 3.25 lb. You take a random sample of 16 containers. You calculate the sample average to be 3.238 lb. with a standard deviation of.117 lb. At the.01 level, is the manufacturer correct? 3.25 lb. AloneGroupClass

182. 8 - 182 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution* H 0 : H a :   df  Critical Value(s): Test Statistic: Decision:Conclusion:

183. 8 - 183 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution* H 0 :  = 3.25 H a :   3.25   df  Critical Value(s): Test Statistic: Decision:Conclusion:

184. 8 - 184 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution* H 0 :  = 3.25 H a :   3.25  .01 df  16 - 1 = 15 Critical Value(s): Test Statistic: Decision:Conclusion:

185. 8 - 185 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution* H 0 :  = 3.25 H a :   3.25  .01 df  16 - 1 = 15 Critical Value(s): Test Statistic: Decision:Conclusion:

186. 8 - 186 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution* H 0 :  = 3.25 H a :   3.25  .01 df  16 - 1 = 15 Critical Value(s): Test Statistic: Decision:Conclusion:

187. 8 - 187 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution* H 0 :  = 3.25 H a :   3.25  .01 df  16 - 1 = 15 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.01

188. 8 - 188 © 1998 Prentice-Hall, Inc. Two-Tailed t Test Solution* H 0 :  = 3.25 H a :   3.25  .01 df  16 - 1 = 15 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.01 There is no evidence average is not 3.25

189. 8 - 189 © 1998 Prentice-Hall, Inc. One-Tailed t Test of Mean (Small Sample)

190. 8 - 190 © 1998 Prentice-Hall, Inc. One-Tailed t Test Example Is the average capacity of batteries at least 140 ampere-hours? A random sample of 20 batteries had a mean of 138.47 & a standard deviation of 2.66. Assume a normal distribution. Test at the.05 level.

191. 8 - 191 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution H 0 : H a :  = df = Critical Value(s): Test Statistic: Decision:Conclusion:

192. 8 - 192 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution H 0 :  = 140 H a :  < 140  = df = Critical Value(s): Test Statistic: Decision:Conclusion:

193. 8 - 193 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution H 0 :  = 140 H a :  < 140  =.05 df = 20 - 1 = 19 Critical Value(s): Test Statistic: Decision:Conclusion:

194. 8 - 194 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution H 0 :  = 140 H a :  < 140  =.05 df = 20 - 1 = 19 Critical Value(s): Test Statistic: Decision:Conclusion:

195. 8 - 195 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution H 0 :  = 140 H a :  < 140  =.05 df = 20 - 1 = 19 Critical Value(s): Test Statistic: Decision:Conclusion:

196. 8 - 196 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution H 0 :  = 140 H a :  < 140  =.05 df = 20 - 1 = 19 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05

197. 8 - 197 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution H 0 :  = 140 H a :  < 140  =.05 df = 20 - 1 = 19 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05 There is evidence pop. average is less than 140

198. 8 - 198 © 1998 Prentice-Hall, Inc. One-Tailed t Test Thinking Challenge You’re a marketing analyst for Wal-Mart. Wal-Mart had teddy bears on sale last week. The weekly sales ($ 00) of bears sold in 10 stores was: 8 11 0 4 7 8 10 5 8 3. At the.05 level, is there evidence that the average bear sales per store is more than 5 ($ 00)? AloneGroupClass

199. 8 - 199 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution* H 0 : H a :  = df = Critical Value(s): Test Statistic: Decision:Conclusion:

200. 8 - 200 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution* H 0 :  = 5 H a :  > 5  = df = Critical Value(s): Test Statistic: Decision:Conclusion:

201. 8 - 201 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution* H 0 :  = 5 H a :  > 5  =.05 df = 10 - 1 = 9 Critical Value(s): Test Statistic: Decision:Conclusion:

202. 8 - 202 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution* H 0 :  = 5 H a :  > 5  =.05 df = 10 - 1 = 9 Critical Value(s): Test Statistic: Decision:Conclusion:

203. 8 - 203 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution* H 0 :  = 5 H a :  > 5  =.05 df = 10 - 1 = 9 Critical Value(s): Test Statistic: Decision:Conclusion:

204. 8 - 204 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution* H 0 :  = 5 H a :  > 5  =.05 df = 10 - 1 = 9 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05

205. 8 - 205 © 1998 Prentice-Hall, Inc. One-Tailed t Test Solution* H 0 :  = 5 H a :  > 5  =.05 df = 10 - 1 = 9 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05 There is no evidence average is more than 5

206. 8 - 206 © 1998 Prentice-Hall, Inc. Z Test of Proportion

207. 8 - 207 © 1998 Prentice-Hall, Inc. One Population Tests One Population Z Test (1 & 2 tail) t Test (1 & 2 tail) Large Sample Z Test (1 & 2 tail) MeanProportion Small Sample

208. 8 - 208 © 1998 Prentice-Hall, Inc. One-Sample Z Test for Proportion

209. 8 - 209 © 1998 Prentice-Hall, Inc. One-Sample Z Test for Proportion 1.Assumptions Two categorical outcomes Two categorical outcomes Population follows binomial distribution Population follows binomial distribution Normal approximation can be used Normal approximation can be used does not contain 0 or n does not contain 0 or n

210. 8 - 210 © 1998 Prentice-Hall, Inc. One-Sample Z Test for Proportion 1.Assumptions Two categorical outcomes Two categorical outcomes Population follows binomial distribution Population follows binomial distribution Normal approximation can be used Normal approximation can be used does not contain 0 or n does not contain 0 or n 2.Z-test statistic for proportion Hypothesized population proportion

211. 8 - 211 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Example The present packaging system produces 10% defective cereal boxes. Using a new system, a random sample of 200 boxes had  11 defects. Does the new system produce fewer defects? Test at the.05 level.

212. 8 - 212 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution H 0 : H a :  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

213. 8 - 213 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution H 0 : p =.10 H a : p <.10  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

214. 8 - 214 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution H 0 : p = .10 H a : p <.10  =.05 n = 200 Critical Value(s): Test Statistic: Decision:Conclusion:

215. 8 - 215 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution H 0 : p =.10 H a : p <.10  =.05 n = 200 Critical Value(s): Test Statistic: Decision:Conclusion:

216. 8 - 216 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution H 0 : p =.10 H a : p <.10  =.05 n = 200 Critical Value(s): Test Statistic: Decision:Conclusion:

217. 8 - 217 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution H 0 : p =.10 H a : p <.10  =.05 n = 200 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05

218. 8 - 218 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution H 0 : p =.10 H a : p <.10  =.05 n = 200 Critical Value(s): Test Statistic: Decision:Conclusion: Reject at  =.05 There is evidence new system < 10% defective

219. 8 - 219 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Thinking Challenge You’re an accounting manager. A year-end audit showed 4% of transactions had errors. You implement new procedures. A random sample of 500 transactions had 25 errors. Has the proportion of incorrect transactions changed at the.05 level? AloneGroupClass

220. 8 - 220 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution* H 0 : H a :  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

221. 8 - 221 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution* H 0 : p =.04 H a : p .04  = n = Critical Value(s): Test Statistic: Decision:Conclusion:

222. 8 - 222 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution* H 0 : p =.04 H a : p .04  =.05 n = 500 Critical Value(s): Test Statistic: Decision:Conclusion:

223. 8 - 223 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution* H 0 : p =.04 H a : p .04  =.05 n = 500 Critical Value(s): Test Statistic: Decision:Conclusion:

224. 8 - 224 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution* H 0 : p =.04 H a : p .04  =.05 n = 500 Critical Value(s): Test Statistic: Decision:Conclusion:

225. 8 - 225 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution* H 0 : p =.04 H a : p .04  =.05 n = 500 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05

226. 8 - 226 © 1998 Prentice-Hall, Inc. One-Proportion Z Test Solution* H 0 : p =.04 H a : p .04  =.05 n = 500 Critical Value(s): Test Statistic: Decision:Conclusion: Do not reject at  =.05 There is evidence proportion is still 4%

227. 8 - 227 © 1998 Prentice-Hall, Inc. 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

228. 8 - 228 © 1998 Prentice-Hall, Inc. This Class... 1.What was the most important thing you learned in class today? 2.What do you still have questions about? 3.How can today’s class be improved? Please take a moment to answer the following questions in writing:

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