Introduction to Sampling Distributions参考.ppt

Chapter 6Introduction to Sampling Distributions Chapter Goals After completing this chapter, you should be able to: Define the concept of sampling error Determine the mean and standard deviation for the sampling distribution of the sample mean, x Determine the mean and standard deviation for the sampling distribution of the sample proportion, p Describe the Central Limit Theorem and its importance Apply sampling distributions for both x and p Sampling Error Sample Statistics are used to estimate Population Parameters ex: X is an estimate of the population mean, μ Problems: Different samples provide different estimates of the population parameter Sample results have potential variability, thus sampling error exits Calculating Sampling Error Sampling Error: The difference between a value (a statistic) computed from a sample and the corresponding value (a parameter) computed from a population Example: (for the mean) where: Review Population mean: Sample Mean: Example Sampling Errors Different samples will yield different sampling errors The sampling error may be positive or negative ( may be greater than or less than μ) The expected sampling error decreases as the sample size increases Sampling Distribution A sampling distribution is a distribution of the possible values of a statistic for a given size sample selected from a population Developing a Sampling Distribution Assume there is a population … Population size N=4 Random variable, x,is age of individuals Values of x: 18, 20,22, 24 (years) Developing a Sampling Distribution Now consider all possible samples of size n=2 Sampling Distribution of All Sample Means Summary Measures of this Sampling Distribution: Comparing the Population with its Sampling Distribution If the Population is Normal z-value for Sampling Distributionof x Z-value for the sampling distribution of : Finite Population Correction Apply the Finite Population Correction if: the sample is large relative to the p