Chapter 6.2（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 6.2 Confidence Intervals for the Mean ( Unknown) . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 6.2 Objectives How to interpret the t-distribution and use a t-distribution table How to construct and interpret confidence intervals for a population mean when  is not known . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. The t-Distribution When the population standard deviation is unknown, the sample size is less than 30, and the random variable x is approximately normally distributed, it follows a t-distribution. Critical values of t are denoted by tc. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Properties of the t-Distribution The mean, median, and mode of the t-distribution are equal to 0. The t-distribution is bell shaped and symmetric about the mean. The total area under a t-curve is 1. The tails in the t-distribution are “thicker” than those in the standard normal distribution. The standard deviation of the t-distribution varies with the sample size, but it is greater than 1. . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 Properties of the t-Distribution The t-distribution is a family of curves, each determined by a parameter called the degrees of freedom. The degrees of freedom are the number of free choices left after a sample statistic such as is calculated. When you use a t-distribution to estimate a population mean, the degrees of freedom are equal to one less than the sample size. d.f. = n – 1 Degrees of freedom . 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Properties of