1. 4 Hypothesis & Testing

2. CHAPTER OUTLINE 4-1 STATISTICAL INFERENCE 4-2 POINT ESTIMATION 4-3 HYPOTHESIS TESTING 4-3.1 Statistical Hypotheses 4-3.2 Testing Statistical Hypotheses 4-3.3 One-Sided and Two-Sided Hypotheses 4-3.4 General Procedure for Hypothesis Testing

3. 4-4 INFERENCE ON THE MEAN OF A POPULATION, VARIANCE KNOWN 4-4.1 Hypothesis Testing on the Mean 4-4.2 P -Values in Hypothesis Testing 4-4.3 Type II Error and Choice of Sample Size 4-4.4 Large-Sample Test 4-4.5 Some Practical Comments on Hypothesis Testing 4-4.6 Confidence Interval on the Mean

4. 4-5 INFERENCE ON THE MEAN OF A POPULATION, VARIANCE UNKNOWN 4-5.1 Hypothesis Testing on the Mean 4-5.2 P -Value for a t -Test 4-5.3 Computer Solution 4-5.4 Choice of Sample Size 4-5.5 Confidence Interval on the Mean 4-6 INFERENCE ON THE VARIANCE OF A NORMAL POPULATION 4-6.1 Hypothesis Testing on the Variance of a Normal Population 4-6.2 Confidence Interval on the Variance of a Normal Population

5. 4-7 INFERENCE ON A POPULATION PROPORTION 4-7.1 Hypothesis Testing on a Binomial Proportion 4-7.2 Type II Error and Choice of Sample Size 4-7.3 Confidence Interval on a Binomial Proportion 4-8 SUMMARY TABLE OF INFERENCE PROCEDURES FOR A SINGLE SAMPLE 4-9 TESTING FOR GOODNESS OF FIT

6. 4-1 STATISTICAL INFERENCE population sample parameter estimation hypothesis testing

8. 4-2 POINT ESTIMATION point estimates point estimator

16. 4-3 HYPOTHESIS TESTING 4-3.1 Statistical Hypotheses hypothesis hypothesis testing comparative experiment

18. null hypothesis alternative hypothesis two-sided alternative hypothesis one-sided alternative hypothesis test of a hypothesis

19. 4-3.2 Testing Statistical Hypotheses critical region acceptance region. critical values

29. 4-3.3 One-Sided and Two-Sided Hypotheses two-sided test one-sided alternative hypothesis one-tailed tests

30. 4-3.4 General Procedure for Hypothesis Testing This chapter develops hypothesis-testing procedures for many practical problems. Use of the following sequence of steps in applying hypothesis-testing methodology is recommended. 1. From the problem context, identify the parameter of interest. 2. State the null hypothesis, H 0. 3. Specify an appropriate alternative hypothesis, H 1. 4. Choose a significance level . 5. State an appropriate test statistic.

31. General Procedure for Hypothesis Testing Continued 6. State the rejection region for the statistic. 7. Compute any necessary sample quantities, substitute these into the equation for the test statistic, and compute that value. 8. Decide whether or not H 0 should be rejected and report that in the problem context. Steps 1–4 should be completed prior to examination of the sample data. This sequence of steps will be illustrated in subsequent sections.

32. 4-4 INFERENCE ON THE MEAN OF A POPULATION, VARIANCE KNOWN unbiased point estimator

33. 4-4.1 Hypothesis Testing on the Mean sampling distribution test statistic

35. acceptance region critical region or rejection region

37. 4-4.2 P-Values in Hypothesis Testing P -value approach

39. 4-4.3 Type II Error and Choice of Sample Size Finding the Probability of Type II Error 

42. 4-4.4 Large-Sample Test 4-4.5 Some Practical Comments on Hypothesis Testing The Eight-Step Procedure 1. Specify the test statistic to be used (such as z 0 ). 2. Specify the location of the critical region (two-tailed, upper-tailed, or lower-tailed). 3. Specify the criteria for rejection (typically, the value of , or the P-value at which rejection should occur).

43. Statistical Versus Practical Significance statistical significance practical significance

45. The moral of this demonstration is clear: be careful when interpreting the results from hypothesis testing when the sample size is large, because any small departure from the hypothesized value  0 will probably be detected, even when the difference is of little or no practical significance.

46. 4-4.6 Confidence Interval on the Mean interval confidence interval lower- and upper-confidence limits confidence coefficient

48. two-sided confidence interval one-sided confidence interval precision

51. Relationship Between Tests of Hypotheses and Confidence Intervals Confidence Level and Precision of Estimation Choice of Sample Size

54. One-Sided Confidence Intervals

55. 4-5 INFERENCE ON THE MEAN OF A POPULATION, VARIANCE UNKNOWN 4-5.1 Hypothesis Testing on the Mean

60. validity of the assumptions

63. 4-5.2 P-Value for a t-Test

64. 4-5.3 Computer Solution

65. 4-5.4 Choice of Sample Size noncentral t distribution central t distribution operating curve (or OC) curves

66. 4-5.5 Confidence Interval on the Mean

67. 4-6 INFERENCE ON THE VARIANCE OF A NORMAL POPULATION 4-6.1 Hypothesis Testing on the Variance of a Normal Population

71. 4-6.2 Confidence Interval on the Variance of a Normal Population

72. One-Sided Confidence Intervals

73. 4-7 INFERENCE ON A POPULATION PROPORTION 4-7.1 Hypothesis Testing on a Binomial Proportion

75. 4-7.2 Type II Error and Choice of Sample Size

76. 4-7.3 Confidence Interval on a Binomial Proportion standard error of the point estimator

78. Choice of Sample Size

79. One-Sided Confidence Intervals

80. 4-8 SUMMARY TABLE OF INFERENCE PROCEDURES FOR A SINGLE SAMPLE

81. 4-9 TESTING FOR GOODNESS OF FIT probability plotting