Chapter 5.4（课件）- 《统计学基础（英文版）》同步教学（人民大学版）

Chapter Normal Probability Distributions 5 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 1 Larson/Farber 6th ed Chapter 1 Chapter Outline 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 5.4 Sampling Distributions and the Central Limit Theorem 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Section 5.4 Objectives How to find sampling distributions and verify their properties How to interpret the Central Limit Theorem How to apply the Central Limit Theorem to find the probability of a sample mean 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. Sampling Distributions Sampling distribution The probability distribution of a sample statistic that is formed when random samples of size n are repeatedly taken from a population. If the sample statistic is the sample mean, then the distribution is the Sampling distribution of sample means 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 5 Sampling Distribution of Sample Means Population with mean μ, and standard deviation σ Random Sample 1 Random Sample 2 Random Sample 3 Random Sample 4 Random Sample 5 The sampling distribution consists of the values of the sample means, 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 6 The standard deviation of the sample means, , is equal to the population standard deviation, σ divided by the square root of the sample size, n. The mean of the sample means, , is equal to the population mean μ. Properties of Sampling Distributions of Sample Means Called the standard error of the mean. 1 Copyright 2019, 2015, 2012, Pearson Education, Inc. 7 Example: A Sampling Distribution of Sample Means The number of times four people go grocery shopping in a month is given by the population values {1, 3, 5, 7}. A probability histogram for the data is shown. You randomly choose two of the four people, with replacement. List all possible samples of size n = 2 and calculate the mean of eac