Chapter 7.5（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Hypothesis Testing with One Sample 7 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 7.1 Introduction to Hypothesis Testing 7.2 Hypothesis Testing for the Mean ( Known) 7.3 Hypothesis Testing for the Mean ( Unknown) 7.4 Hypothesis Testing for Proportions 7.5 Hypothesis Testing for Variance and Standard Deviation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 7.5 Hypothesis Testing for Variance and Standard Deviation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 7.5 Objectives How to find critical values for a χ2-test How to use the χ2-test to test a variance 2 or a standard deviation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Finding Critical Values for a χ2-Test Specify the level of significance . Determine the degrees of freedom d.f. = n – 1. The critical values for the χ2-distribution are found in Table 6 of Appendix B. To find the critical value(s) for a right-tailed test, use the value that corresponds to d.f. and . left-tailed test, use the value that corresponds to d.f. and 1 – . two-tailed test, use the values that corresponds to d.f. and ½ and d.f. and 1 – ½. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Finding Critical Values for the χ2-Test . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 Example: Finding Critical Values for χ2 Find the critical χ2-value for a left-tailed test when n = 26 and  = 0.10. Solution: The degrees of freedom are d.f. = n – 1 = 26 – 1 = 25. The figure shows a chi-square distribution with 25 degrees of freedom and a shaded area of a = 0.10 in the right tail. . Using Table 6 in App. B with d.f. = 25 and a = 0.10, the critical value is 02 = 34.382. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Example: Finding Critical Values for χ2 Find the critical χ2-value for a left-tailed test when n = 11 and  = 0.01. Solution: The degrees of freedom are d.f. = n – 1 = 11 – 1