Chapter 6.4（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Confidence Intervals 6 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 6.1 Confidence Intervals for the Mean ( Known) 6.2 Confidence Intervals for the Mean ( Unknown) 6.3 Confidence Intervals for Population Proportions 6.4 Confidence Intervals for Variance and Standard Deviation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 6.4 Confidence Intervals for Variance and Standard Deviation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 6.4 Objectives How to interpret the chi-square distribution and use a chi-square distribution table How to construct and interpret confidence intervals for a population variance and standard deviation . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The Chi-Square Distribution The point estimate for  2 is s2 The point estimate for  is s s2 is the most unbiased estimate for 2 Estimate Population Parameter… with Sample Statistic Variance: σ2 s2 Standard deviation: σ s . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 The Chi-Square Distribution You can use the chi-square distribution to construct a confidence interval for the variance and standard deviation. If the random variable x has a normal distribution, then the distribution of forms a chi-square distribution for samples of any size n > 1. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 Properties of The Chi-Square Distribution All chi-square values χ2 are greater than or equal to zero. The chi-square distribution is a family of curves, each determined by the degrees of freedom. To form a confidence interval for 2, use the chi-square distribution with degrees of freedom equal to one less than the sample size. d.f. = n – 1 Degrees of freedom The total area under each chi-square distribution curve is equal to 1. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Properties of The Chi-Square Distribution The chi-square distr