© 2001 Prentice-Hall, Inc.Chap 7-1 BA 201 Lecture 11 Sampling Distributions

© 2001 Prentice-Hall, Inc. Chap 7-2 Topics Estimation Process Point Estimates Interval Estimates Sampling Distribution of the Mean

© 2001 Prentice-Hall, Inc. Chap 7-3 Population and Sample PopulationSample Use parameters to summarize features Use statistics to summarize features Inference on the population from the sample p.??

© 2001 Prentice-Hall, Inc. Chap 7-4 Estimation Process Mean, , is unknown PopulationRandom Sample I conjecture that the population mean, , is 50 Sample pp.??

© 2001 Prentice-Hall, Inc. Chap 7-5 Point Estimates Estimate Population Parameters … with Sample Statistics Mean Proportion Variance Difference p.267

© 2001 Prentice-Hall, Inc. Chap 7-6 Another Point Estimate Here is a link to some of the most recent poll results Here

© 2001 Prentice-Hall, Inc. Chap 7-7 Drawback of Point Estimates Q. What is the probability that a point estimate will equal to the true parameter that is being estimated? A. Zero. Theoretically, you will never obtain a point estimate that equals the unknown parameter. p.?

© 2001 Prentice-Hall, Inc. Chap 7-8 Interval Estimation Process Mean, , is unknown PopulationRandom Sample I am 95% confident that  is between 40 & 60. Sample pp.??

© 2001 Prentice-Hall, Inc. Chap 7-9 Interval Estimates Provides Range of Values Take into consideration variation in sample statistics from sample to sample Based on observation from 1 sample Give Information about Closeness to Unknown Population Parameters Stated in terms of level of confidence Never 100% sure p.267

© 2001 Prentice-Hall, Inc. Chap 7-10 Confidence Interval Estimates Mean  Unknown Confidence Intervals Proportion  Known pp.??

© 2001 Prentice-Hall, Inc. Chap 7-11 Why Study Sampling Distributions Sample Statistics are Used to Estimate Population Parameters E.g. estimates the population mean Problems: Different Sample Provides Different Estimate Large sample gives better estimate; large sample costs more How good is the estimate? Approach to Solution: Theoretical Basis is Sampling Distribution p.252

© 2001 Prentice-Hall, Inc. Chap 7-12 Sampling Distribution Theoretical Probability Distribution of a Sample Statistic Sample Statistic is a Random Variable Sample mean, sample proportion Results from Taking All Possible Samples of the Same Size p.252

© 2001 Prentice-Hall, Inc. Chap 7-13 When the Population is Normal Central Tendency Variation Sampling with Replacement Population Distribution Sampling Distributions pp

© 2001 Prentice-Hall, Inc. Chap 7-14 When the Population is Not Normal Central Tendency Variation Sampling with Replacement Population Distribution Sampling Distributions pp

© 2001 Prentice-Hall, Inc. Chap 7-15 Central Limit Theorem As Sample Size Gets Large Enough Sampling Distribution Becomes Almost Normal Regardless of Shape of Population p.261

© 2001 Prentice-Hall, Inc. Chap 7-16 Applet to Illustrate the CLT Click here to access the applet that will illustrate the Central Limit Theorem in action.here

© 2001 Prentice-Hall, Inc. Chap 7-17 How Large is Large Enough? For Most Distributions, n>30 For Fairly Symmetric Distributions, n>15 For Normal Distribution, the Sampling Distribution of the Mean is Always Normally Distributed This is a property of sampling from a normal population distribution and is NOT a result of the central limit theorem p.265

© 2001 Prentice-Hall, Inc. Chap 7-18 Summary Illustrated Estimation Process Discussed Point Estimates Addressed Interval Estimates Discussed Sampling Distribution of the Sample Mean