© 2002 Thomson / South-Western Slide 8-1 Chapter 8 Estimation with Single Samples.

Slides:

Advertisements

Similar presentations

Estimating a Population Variance

Advertisements

Business Statistics, 4e, by Ken Black. © 2003 John Wiley & Sons. 8-1 Business Statistics, 4e by Ken Black Chapter 8 Statistical Inference: Estimation for.

Sampling: Final and Initial Sample Size Determination

Chap 8-1 Statistics for Business and Economics, 6e © 2007 Pearson Education, Inc. Chapter 8 Estimation: Single Population Statistics for Business and Economics.

1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Section 7.5 Estimation of a Population Variance This section presents methods.

Single Sample t-test Purpose: Compare a sample mean to a hypothesized population mean. Design: One group.

BCOR 1020 Business Statistics Lecture 17 – March 18, 2008.

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 7-1 Chapter 7 Confidence Interval Estimation Statistics for Managers.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 8-1 Chapter 8 Confidence Interval Estimation Basic Business Statistics 10 th Edition.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 7-1 Introduction to Statistics: Chapter 8 Estimation.

Chapter 8 Estimation: Single Population

Chapter Topics Confidence Interval Estimation for the Mean (s Known)

Fall 2006 – Fundamentals of Business Statistics 1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter 7 Estimating Population Values.

Chapter 7 Estimating Population Values

1 (Student’s) T Distribution. 2 Z vs. T Many applications involve making conclusions about an unknown mean . Because a second unknown, , is present,

Copyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc. Chapter 7 Statistical Intervals Based on a Single Sample.

Business Statistics, A First Course (4e) © 2006 Prentice-Hall, Inc. Chap 8-1 Chapter 8 Confidence Interval Estimation Business Statistics, A First Course.

Confidence Intervals for the Mean (σ Unknown) (Small Samples)

Statistics for Managers Using Microsoft Excel, 4e © 2004 Prentice-Hall, Inc. Chap 7-1 Chapter 7 Confidence Interval Estimation Statistics for Managers.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 7-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter.

Confidence Interval Estimation

Confidence Intervals (Chapter 8) Confidence Intervals for numerical data: –Standard deviation known –Standard deviation unknown Confidence Intervals for.

CONFIDENCE INTERVALS of Means AP STATISTICS, CHAPTER 19 Mrs. Watkins.

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 8-1 Confidence Interval Estimation.

Confidence Intervals for Means. point estimate – using a single value (or point) to approximate a population parameter. –the sample mean is the best point.

Chapter 9 Hypothesis Testing and Estimation for Two Population Parameters.

1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Chapter 11 Inferences About Population Variances n Inference about a Population Variance n.

© 2002 Thomson / South-Western Slide 10-1 Chapter 10 Hypothesis Testing with Two Samples.

Slide 1 © 2002 McGraw-Hill Australia, PPTs t/a Introductory Mathematics & Statistics for Business 4e by John S. Croucher 1 n Learning Objectives –Identify.

H1H1 H1H1 HoHo Z = 0 Two Tailed test. Z score where 2.5% of the distribution lies in the tail: Z = Critical value for a two tailed test.

CHAPTER SIX Confidence Intervals.

Determination of Sample Size: A Review of Statistical Theory

Chap 7-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In Business Statistics 4 th Edition Chapter 7 Estimating Population Values.

Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc. Chap 8-1 Confidence Interval Estimation.

The Single-Sample t Test Chapter 9. The t Distributions >Distributions of Means When the Parameters Are Not Known >Using t distributions Estimating a.

Section 7-3 Estimating a Population Mean: σ Known.

CHAPTER SIX Confidence Intervals.

Confidence Intervals for the Mean (Small Samples) 1 Larson/Farber 4th ed.

Chap 7-1 A Course In Business Statistics, 4th © 2006 Prentice-Hall, Inc. A Course In Business Statistics 4 th Edition Chapter 7 Estimating Population Values.

Statistics for Business and Economics 8 th Edition Chapter 7 Estimation: Single Population Copyright © 2013 Pearson Education, Inc. Publishing as Prentice.

Copyright © 1998, Triola, Elementary Statistics Addison Wesley Longman 1 Estimates and Sample Sizes Chapter 6 M A R I O F. T R I O L A Copyright © 1998,

1 1 Slide © 2007 Thomson South-Western. All Rights Reserved Chapter 8 Interval Estimation Population Mean:  Known Population Mean:  Known Population.

Copyright ©2013 Pearson Education, Inc. publishing as Prentice Hall

 A Characteristic is a measurable description of an individual such as height, weight or a count meeting a certain requirement.  A Parameter is a numerical.

Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 7-1 Business Statistics: A Decision-Making Approach 6 th Edition Chapter.

Point Estimates point estimate A point estimate is a single number determined from a sample that is used to estimate the corresponding population parameter.

Section 6.2 Confidence Intervals for the Mean (Small Samples) Larson/Farber 4th ed.

Business Statistics: Contemporary Decision Making, 3e, by Black. © 2001 South-Western/Thomson Learning 8-1 Business Statistics, 3e by Ken Black Chapter.

Chapter 8 Single Sample Tests Part II: Introduction to Hypothesis Testing Renee R. Ha, Ph.D. James C. Ha, Ph.D Integrative Statistics for the Social &

ESTIMATION OF THE MEAN. 2 INTRO :: ESTIMATION Definition The assignment of plausible value(s) to a population parameter based on a value of a sample statistic.

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 8-1 Chapter 8 Confidence Interval Estimation Business Statistics: A First Course 5 th Edition.

Section 6.2 Confidence Intervals for the Mean (Small Samples) © 2012 Pearson Education, Inc. All rights reserved. 1 of 83.

Chapter 8 Confidence Intervals Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin.

Chapter 8 Confidence Interval Estimation Statistics For Managers 5 th Edition.

Chapter 7 Estimation. Chapter 7 ESTIMATION What if it is impossible or impractical to use a large sample? Apply the Student ’ s t distribution.

CHAPTER 8 Estimating with Confidence

CHAPTER 8 Estimating with Confidence

Estimation and Confidence Intervals

Chapter 6 Inferences Based on a Single Sample: Estimation with Confidence Intervals Slides for Optional Sections Section 7.5 Finite Population Correction.

Chapter 6 Confidence Intervals.

Statistical Inference: Estimation for Single Populations

Introduction to Inference

Elementary Statistics

Business Statistics, 5th ed. by Ken Black

WARM - UP 1. How do you interpret a Confidence Interval?

Chapter 6 Confidence Intervals.

Confidence Interval Estimation

Chapter 6 Confidence Intervals.

Statistical Inference for the Mean: t-test

Chapter 7 Estimation: Single Population

Presentation transcript:

© 2002 Thomson / South-Western Slide 8-1 Chapter 8 Estimation with Single Samples

© 2002 Thomson / South-Western Slide 8-2 Learning Objectives Know the difference between point and interval estimation. Estimate a population mean from a sample mean for large sample sizes. Estimate a population mean from a sample mean for small sample sizes. Estimate a population proportion from a sample proportion. Estimate the minimum sample size necessary to achieve given statistical goals.

© 2002 Thomson / South-Western Slide 8-3 Statistical Estimation Point estimate -- the single value of a statistic calculated from a sample Interval Estimate -- a range of values calculated from a sample statistic(s) and standardized statistics, such as the Z. –Selection of the standardized statistic is determined by the sampling distribution. –Selection of critical values of the standardized statistic is determined by the desired level of confidence.

© 2002 Thomson / South-Western Slide 8-4 Confidence Interval to Estimate  when n is Large Point estimate Interval Estimate

© 2002 Thomson / South-Western Slide 8-5 Distribution of Sample Means for (1-  )% Confidence  X  Z 0

© 2002 Thomson / South-Western Slide 8-6 Z Scores for Confidence Intervals in Relation to   X Z 0

© 2002 Thomson / South-Western Slide 8-7 Distribution of Sample Means for (1-  )% Confidence  X Z 0

© 2002 Thomson / South-Western Slide 8-8 Probability Interpretation of the Level of Confidence

© 2002 Thomson / South-Western Slide 8-9 Distribution of Sample Means for 95% Confidence .4750 X 95%.025 Z

© 2002 Thomson / South-Western Slide 8-10 Example: 95% Confidence Interval for 

© 2002 Thomson / South-Western Slide % Confidence Intervals for   X 95% X X X X X X

© 2002 Thomson / South-Western Slide % Confidence Intervals for   X 95% X X X X X X Is our interval, 3.98  4.54, in the red?

© 2002 Thomson / South-Western Slide 8-13 Demonstration Problem 8.1

© 2002 Thomson / South-Western Slide 8-14 Demonstration Problem 8.2

© 2002 Thomson / South-Western Slide 8-15 Confidence Interval to Estimate  when n is Large and  is Unknown

© 2002 Thomson / South-Western Slide 8-16 Z Values for Some of the More Common Levels of Confidence 90% 95% 98% 99% Confidence Level Z Value

© 2002 Thomson / South-Western Slide 8-17 Estimating the Mean of a Normal Population: Small n and Unknown  The population has a normal distribution. The value of the population standard deviation is unknown. The sample size is small, n < 30. Z distribution is not appropriate for these conditions t distribution is appropriate

© 2002 Thomson / South-Western Slide 8-18 The t Distribution A family of distributions -- a unique distribution for each value of its parameter, degrees of freedom (d.f.) Symmetric, Unimodal, Mean = 0, Flatter than a Z t formula

© 2002 Thomson / South-Western Slide 8-19 Comparison of Selected t Distributions to the Standard Normal Standard Normal t (d.f. = 25) t (d.f. = 5) t (d.f. = 1)

© 2002 Thomson / South-Western Slide 8-20 Table of Critical Values of t df t t t t t  tt  

© 2002 Thomson / South-Western Slide 8-21 Confidence Intervals for  of a Normal Population: Small n and Unknown 

© 2002 Thomson / South-Western Slide 8-22 Solution for Demonstration Problem 8.3

© 2002 Thomson / South-Western Slide 8-23 Solution for Demonstration Problem 8.3

© 2002 Thomson / South-Western Slide 8-24 Confidence Interval to Estimate the Population Proportion

© 2002 Thomson / South-Western Slide 8-25 Solution for Demonstration Problem 8.5

© 2002 Thomson / South-Western Slide 8-26 Determining Sample Size when Estimating  Z formula Error of Estimation (tolerable error) Estimated Sample Size Estimated 

© 2002 Thomson / South-Western Slide 8-27 Example: Sample Size when Estimating 

© 2002 Thomson / South-Western Slide 8-28 Solution for Demonstration Problem 8.6

© 2002 Thomson / South-Western Slide 8-29 Determining Sample Size when Estimating P Z formula Error of Estimation (tolerable error) Estimated Sample Size

© 2002 Thomson / South-Western Slide 8-30 Solution for Demonstration Problem 8.7

© 2002 Thomson / South-Western Slide 8-31 Determining Sample Size when Estimating P with No Prior Information P n Z = 1.96 E = 0.05 P PQ

© 2002 Thomson / South-Western Slide 8-32 Solution for Demonstration Problem 8.8