Chapter 7.3（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 7.3 Hypothesis Testing for the Mean ( Unknown) . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 7.3 Objectives Find critical values in a t-distribution Use the t-test to test a mean μ when σ is not known Use technology to find P-values and use them with a t-test to test a mean μ when σ is not known . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Finding Critical Values in a t-Distribution Identify the level of significance . Identify the degrees of freedom d.f. = n – 1. Find the critical value(s) using Table 5 in Appendix B in the row with n – 1 degrees of freedom. If the hypothesis test is left-tailed, use “One Tail,  ” column with a negative sign, right-tailed, use “One Tail,  ” column with a positive sign, two-tailed, use “Two Tails,  ” column with a negative and a positive sign. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Finding Critical Values in a t-Distribution . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 Example: Finding Critical Values for t Find the critical value t0 for a left-tailed test given  = 0.05 and n = 21. Solution: The degrees of freedom are d.f. = n – 1 = 21 – 1 = 20. Use Table 5. Look at α = 0.05 in the “One Tail, ” column. Because the test is left-tailed, the critical value is negative. So, t0 = – 1.725. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Example: Finding Critical Values for t Find the critical value t0 for a right-tailed test given  = 0.01 and n = 17. Solution: The degrees of freedom are d.f. = n – 1 = 17 – 1 = 16