1 1 Slide © 2005 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University.

Slides:



Advertisements
Similar presentations
Statistics for Managers Using Microsoft® Excel 5th Edition
Advertisements

Sampling and Sampling Distribution
1 1 Slide 2009 University of Minnesota-Duluth, Econ-2030(Dr. Tadesse) Chapter 7, Part B Sampling and Sampling Distributions Other Sampling Methods Other.
Chapter 7 Sampling Distributions
1 1 Slide © 2003 South-Western/Thomson Learning™ Slides Prepared by JOHN S. LOUCKS St. Edward’s University.
Why sample? Diversity in populations Practicality and cost.
Sampling and Sampling Distributions: Part 2 Sample size and the sampling distribution of Sampling distribution of Sampling methods.
Sampling and Sampling Distributions Simple Random Sampling Point Estimation Sampling Distribution.
1 1 Slide © 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole.
QMS 6351 Statistics and Research Methods Chapter 7 Sampling and Sampling Distributions Prof. Vera Adamchik.
The Excel NORMDIST Function Computes the cumulative probability to the value X Business Statistics: A First Course, 5e © 2009 Prentice-Hall, Inc
7/2/2015 (c) 2001, Ron S. Kenett, Ph.D.1 Sampling for Estimation Instructor: Ron S. Kenett Course Website:
7-1 Copyright ©2011 Pearson Education, Inc. publishing as Prentice Hall Chapter 7 Sampling and Sampling Distributions Statistics for Managers using Microsoft.
Chapter 7 Sampling and Sampling Distributions Sampling Distribution of Sampling Distribution of Introduction to Sampling Distributions Introduction to.
SAMPLING: Process of Selecting your Observations
1 1 Slide Slides Prepared by JOHN S. LOUCKS St. Edward’s University © 2002 South-Western College Publishing/Thomson Learning.
SAMPLING AND SAMPLING DISTRIBUTIONS
Sample Design.
Chapter 7 Sampling and Sampling Distributions n Simple Random Sampling n Point Estimation n Introduction to Sampling Distributions n Sampling Distribution.
1 1 Slide © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole.
Sampling.
1 1 Slide © 2009 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.
Sampling: Theory and Methods
1 1 Slide Slides Prepared by JOHN S. LOUCKS St. Edward’s University © 2002 South-Western/Thomson Learning.
1 1 Slide © 2003 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University.
1 1 Slide © 2004 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University.
1 1 Slide © 2001 South-Western/Thomson Learning  Anderson  Sweeney  Williams Anderson  Sweeney  Williams  Slides Prepared by JOHN LOUCKS  CONTEMPORARYBUSINESSSTATISTICS.
Chapter 7 Sampling and Sampling Distributions Sampling Distribution of Sampling Distribution of Introduction to Sampling Distributions Introduction to.
Sampling The sampling errors are: for sample mean
1 1 Slide © 2009 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.
1 1 Slide © 2009 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.
1 1 Slide © 2005 Thomson/South-Western Chapter 7, Part A Sampling and Sampling Distributions Sampling Distribution of Sampling Distribution of Introduction.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.
1 1 Slide Chapter 7 (b) – Point Estimation and Sampling Distributions Point estimation is a form of statistical inference. Point estimation is a form of.
1 1 Slide IS 310 – Business Statistics IS 310 Business Statistics CSU Long Beach.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.
1 1 Slide © 2008 Thomson South-Western. All Rights Reserved Slides by JOHN LOUCKS St. Edward’s University.
1 1 Slide © 2007 Thomson South-Western. All Rights Reserved OPIM 303-Lecture #5 Jose M. Cruz Assistant Professor.
1 1 Slide © 2007 Thomson South-Western. All Rights Reserved Chapter 7 Sampling and Sampling Distributions Sampling Distribution of Sampling Distribution.
Copyright ©2011 Pearson Education 7-1 Chapter 7 Sampling and Sampling Distributions Statistics for Managers using Microsoft Excel 6 th Global Edition.
Agricultural and Biological Statistics. Sampling and Sampling Distributions Chapter 5.
1 1 Slide Sampling and Sampling Distributions Sampling Distribution of Sampling Distribution of Introduction to Sampling Distributions Introduction to.
1 Chapter 7 Sampling and Sampling Distributions Simple Random Sampling Point Estimation Introduction to Sampling Distributions Sampling Distribution of.
Econ 3790: Business and Economics Statistics Instructor: Yogesh Uppal
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
Sampling Methods. Probability Sampling Techniques Simple Random Sampling Cluster Sampling Stratified Sampling Systematic Sampling Copyright © 2012 Pearson.
1 Chapter 7 Sampling Distributions. 2 Chapter Outline  Selecting A Sample  Point Estimation  Introduction to Sampling Distributions  Sampling Distribution.
1 1 Slide STATISTICS FOR BUSINESS AND ECONOMICS Seventh Edition AndersonSweeneyWilliams Slides Prepared by John Loucks © 1999 ITP/South-Western College.
1 1 Slide © 2003 South-Western/Thomson Learning™ Slides Prepared by JOHN S. LOUCKS St. Edward’s University.
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Chapter 7 Sampling and Sampling Distributions.
Basic Business Statistics, 10e © 2006 Prentice-Hall, Inc.. Chap 7-1 Chapter 7 Sampling Distributions Basic Business Statistics.
Statistics for Managers Using Microsoft Excel, 5e © 2008 Pearson Prentice-Hall, Inc.Chap 7-1 Statistics for Managers Using Microsoft® Excel 5th Edition.
15-1 Chapter 15 Sampling Learning Objectives Understand... two premises on which sampling theory is based accuracy and precision for measuring sample.
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 7-1 Chapter 7 Sampling and Sampling Distributions Basic Business Statistics 11 th Edition.
McGraw-Hill/IrwinCopyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. SAMPLING Chapter 14.
Basic Business Statistics
Sampling Design and Procedure
Fundamentals of Business Statistics chapter7 Sampling and Sampling Distributions 上海金融学院统计系 Statistics Dept., Shanghai Finance University.
Sampling Why use sampling? Terms and definitions
Chapter 7 (b) – Point Estimation and Sampling Distributions
St. Edward’s University
Sampling and Sampling Distribution
Graduate School of Business Leadership
John Loucks St. Edward’s University . SLIDES . BY.
Chapter 5, Part A [SBE 7/e, Ch. 7] Sampling and Sampling Distributions
Slides by JOHN LOUCKS St. Edward’s University.
Chapter 7 Sampling Distributions
Chapter 7 Sampling and Sampling Distributions
Presentation transcript:

1 1 Slide © 2005 Thomson/South-Western Slides Prepared by JOHN S. LOUCKS St. Edward’s University Slides Prepared by JOHN S. LOUCKS St. Edward’s University

2 2 Slide © 2005 Thomson/South-Western Chapter 7, Part B Sampling and Sampling Distributions Other Sampling Methods Other Sampling Methods Sampling Distribution of Sampling Distribution of Properties of Point Estimators Properties of Point Estimators

3 3 Slide © 2005 Thomson/South-Western A simple random sample of n elements is selected from the population. Population with proportion p = ? n Making Inferences about a Population Proportion The sample data provide a value for the sample proportion. The value of is used to make inferences about the value of p. Sampling Distribution of

4 4 Slide © 2005 Thomson/South-Western Sampling Distribution of where: p = the population proportion The sampling distribution of is the probability distribution of all possible values of the sample proportion. Expected Value of

5 5 Slide © 2005 Thomson/South-Western is referred to as the standard error of the is referred to as the standard error of the proportion. Sampling Distribution of Finite Population Infinite Population Standard Deviation of

6 6 Slide © 2005 Thomson/South-Western The sampling distribution of can be approximated The sampling distribution of can be approximated by a normal distribution whenever the sample size by a normal distribution whenever the sample size is large. is large. The sample size is considered large whenever these The sample size is considered large whenever these conditions are satisfied: conditions are satisfied: np > 5 n (1 – p ) > 5 and Form of the Sampling Distribution of

7 7 Slide © 2005 Thomson/South-Western For values of p near.50, sample sizes as small as 10 permit a normal approximation. With very small (approaching 0) or very large (approaching 1) values of p, much larger samples are needed. Form of the Sampling Distribution of

8 8 Slide © 2005 Thomson/South-Western Recall that 72% of the Recall that 72% of the prospective students applying to St. Andrew’s College desire on-campus housing. n Example: St. Andrew’s College Sampling Distribution of What is the probability that What is the probability that a simple random sample of 30 applicants will provide an estimate of the population proportion of applicant desiring on-campus housing that is within plus or minus.05 of the actual population proportion?

9 9 Slide © 2005 Thomson/South-Western For our example, with n = 30 and p =.72, the normal distribution is an acceptable approximation because: n (1 - p ) = 30(.28) = 8.4 > 5 and np = 30(.72) = 21.6 > 5 Sampling Distribution of

10 Slide © 2005 Thomson/South-Western SamplingDistributionof Sampling Distribution of

11 Slide © 2005 Thomson/South-Western Step 1: Calculate the z -value at the upper endpoint of the interval. the interval. z = (.77 .72)/.082 =.61 P ( z <.61) =.7291 Step 2: Find the area under the curve to the left of the upper endpoint. upper endpoint. Sampling Distribution of

12 Slide © 2005 Thomson/South-Western Cumulative Probabilities for the Standard Normal Distribution the Standard Normal Distribution Sampling Distribution of

13 Slide © 2005 Thomson/South-Western Area =.7291 SamplingDistributionof Sampling Distribution of

14 Slide © 2005 Thomson/South-Western Step 3: Calculate the z -value at the lower endpoint of the interval. the interval. Step 4: Find the area under the curve to the left of the lower endpoint. lower endpoint. z = (.67 .72)/.082 = -.61 P ( z.61) =.2709 = 1  = 1  P ( z <.61) Sampling Distribution of

15 Slide © 2005 Thomson/South-Western Area =.2709 SamplingDistributionof Sampling Distribution of

16 Slide © 2005 Thomson/South-Western P (.67 < <.77) =.4582 Step 5: Calculate the area under the curve between the lower and upper endpoints of the interval. the lower and upper endpoints of the interval. P (-.61 < z <.61) = P ( z <.61)  P ( z < -.61) =.7291 .2709 =.4582 The probability that the sample proportion of applicants wanting on-campus housing will be within +/-.05 of the actual population proportion : Sampling Distribution of

17 Slide © 2005 Thomson/South-Western Area =.4582 SamplingDistributionof Sampling Distribution of

18 Slide © 2005 Thomson/South-Western Properties of Point Estimators n Before using a sample statistic as a point estimator, statisticians check to see whether the sample statistic has the following properties associated with good point estimators. Consistency Efficiency Unbiased

19 Slide © 2005 Thomson/South-Western Properties of Point Estimators If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to be an unbiased estimator of the population parameter. Unbiased

20 Slide © 2005 Thomson/South-Western Properties of Point Estimators Given the choice of two unbiased estimators of the same population parameter, we would prefer to use the point estimator with the smaller standard deviation, since it tends to provide estimates closer to the population parameter. The point estimator with the smaller standard deviation is said to have greater relative efficiency than the other. Efficiency

21 Slide © 2005 Thomson/South-Western Properties of Point Estimators A point estimator is consistent if the values of the point estimator tend to become closer to the population parameter as the sample size becomes larger. Consistency

22 Slide © 2005 Thomson/South-Western Other Sampling Methods n Stratified Random Sampling n Cluster Sampling n Systematic Sampling n Convenience Sampling n Judgment Sampling

23 Slide © 2005 Thomson/South-Western The population is first divided into groups of The population is first divided into groups of elements called strata. elements called strata. The population is first divided into groups of The population is first divided into groups of elements called strata. elements called strata. Stratified Random Sampling Each element in the population belongs to one and Each element in the population belongs to one and only one stratum. only one stratum. Each element in the population belongs to one and Each element in the population belongs to one and only one stratum. only one stratum. Best results are obtained when the elements within Best results are obtained when the elements within each stratum are as much alike as possible each stratum are as much alike as possible (i.e. a homogeneous group). (i.e. a homogeneous group). Best results are obtained when the elements within Best results are obtained when the elements within each stratum are as much alike as possible each stratum are as much alike as possible (i.e. a homogeneous group). (i.e. a homogeneous group).

24 Slide © 2005 Thomson/South-Western Stratified Random Sampling A simple random sample is taken from each stratum. A simple random sample is taken from each stratum. Formulas are available for combining the stratum Formulas are available for combining the stratum sample results into one population parameter sample results into one population parameter estimate. estimate. Formulas are available for combining the stratum Formulas are available for combining the stratum sample results into one population parameter sample results into one population parameter estimate. estimate. Advantage: If strata are homogeneous, this method Advantage: If strata are homogeneous, this method is as “precise” as simple random sampling but with is as “precise” as simple random sampling but with a smaller total sample size. a smaller total sample size. Advantage: If strata are homogeneous, this method Advantage: If strata are homogeneous, this method is as “precise” as simple random sampling but with is as “precise” as simple random sampling but with a smaller total sample size. a smaller total sample size. Example: The basis for forming the strata might be Example: The basis for forming the strata might be department, location, age, industry type, and so on. department, location, age, industry type, and so on. Example: The basis for forming the strata might be Example: The basis for forming the strata might be department, location, age, industry type, and so on. department, location, age, industry type, and so on.

25 Slide © 2005 Thomson/South-Western Cluster Sampling The population is first divided into separate groups The population is first divided into separate groups of elements called clusters. of elements called clusters. The population is first divided into separate groups The population is first divided into separate groups of elements called clusters. of elements called clusters. Ideally, each cluster is a representative small-scale Ideally, each cluster is a representative small-scale version of the population (i.e. heterogeneous group). version of the population (i.e. heterogeneous group). Ideally, each cluster is a representative small-scale Ideally, each cluster is a representative small-scale version of the population (i.e. heterogeneous group). version of the population (i.e. heterogeneous group). A simple random sample of the clusters is then taken. A simple random sample of the clusters is then taken. All elements within each sampled (chosen) cluster All elements within each sampled (chosen) cluster form the sample. form the sample. All elements within each sampled (chosen) cluster All elements within each sampled (chosen) cluster form the sample. form the sample.

26 Slide © 2005 Thomson/South-Western Cluster Sampling Advantage: The close proximity of elements can be Advantage: The close proximity of elements can be cost effective (i.e. many sample observations can be cost effective (i.e. many sample observations can be obtained in a short time). obtained in a short time). Advantage: The close proximity of elements can be Advantage: The close proximity of elements can be cost effective (i.e. many sample observations can be cost effective (i.e. many sample observations can be obtained in a short time). obtained in a short time). Disadvantage: This method generally requires a Disadvantage: This method generally requires a larger total sample size than simple or stratified larger total sample size than simple or stratified random sampling. random sampling. Disadvantage: This method generally requires a Disadvantage: This method generally requires a larger total sample size than simple or stratified larger total sample size than simple or stratified random sampling. random sampling. Example: A primary application is area sampling, Example: A primary application is area sampling, where clusters are city blocks or other well-defined where clusters are city blocks or other well-defined areas. areas. Example: A primary application is area sampling, Example: A primary application is area sampling, where clusters are city blocks or other well-defined where clusters are city blocks or other well-defined areas. areas.

27 Slide © 2005 Thomson/South-Western Systematic Sampling If a sample size of n is desired from a population If a sample size of n is desired from a population containing N elements, we might sample one containing N elements, we might sample one element for every n / N elements in the population. element for every n / N elements in the population. If a sample size of n is desired from a population If a sample size of n is desired from a population containing N elements, we might sample one containing N elements, we might sample one element for every n / N elements in the population. element for every n / N elements in the population. We randomly select one of the first n / N elements We randomly select one of the first n / N elements from the population list. from the population list. We randomly select one of the first n / N elements We randomly select one of the first n / N elements from the population list. from the population list. We then select every n / N th element that follows in We then select every n / N th element that follows in the population list. the population list. We then select every n / N th element that follows in We then select every n / N th element that follows in the population list. the population list.

28 Slide © 2005 Thomson/South-Western Systematic Sampling This method has the properties of a simple random This method has the properties of a simple random sample, especially if the list of the population sample, especially if the list of the population elements is a random ordering. elements is a random ordering. This method has the properties of a simple random This method has the properties of a simple random sample, especially if the list of the population sample, especially if the list of the population elements is a random ordering. elements is a random ordering. Advantage: The sample usually will be easier to Advantage: The sample usually will be easier to identify than it would be if simple random sampling identify than it would be if simple random sampling were used. were used. Advantage: The sample usually will be easier to Advantage: The sample usually will be easier to identify than it would be if simple random sampling identify than it would be if simple random sampling were used. were used. Example: Selecting every 100 th listing in a telephone Example: Selecting every 100 th listing in a telephone book after the first randomly selected listing book after the first randomly selected listing Example: Selecting every 100 th listing in a telephone Example: Selecting every 100 th listing in a telephone book after the first randomly selected listing book after the first randomly selected listing

29 Slide © 2005 Thomson/South-Western Convenience Sampling It is a nonprobability sampling technique. Items are It is a nonprobability sampling technique. Items are included in the sample without known probabilities included in the sample without known probabilities of being selected. of being selected. It is a nonprobability sampling technique. Items are It is a nonprobability sampling technique. Items are included in the sample without known probabilities included in the sample without known probabilities of being selected. of being selected. Example: A professor conducting research might use Example: A professor conducting research might use student volunteers to constitute a sample. student volunteers to constitute a sample. Example: A professor conducting research might use Example: A professor conducting research might use student volunteers to constitute a sample. student volunteers to constitute a sample. The sample is identified primarily by convenience. The sample is identified primarily by convenience.

30 Slide © 2005 Thomson/South-Western Advantage: Sample selection and data collection are Advantage: Sample selection and data collection are relatively easy. relatively easy. Advantage: Sample selection and data collection are Advantage: Sample selection and data collection are relatively easy. relatively easy. Disadvantage: It is impossible to determine how Disadvantage: It is impossible to determine how representative of the population the sample is. representative of the population the sample is. Disadvantage: It is impossible to determine how Disadvantage: It is impossible to determine how representative of the population the sample is. representative of the population the sample is. Convenience Sampling

31 Slide © 2005 Thomson/South-Western Judgment Sampling The person most knowledgeable on the subject of the The person most knowledgeable on the subject of the study selects elements of the population that he or study selects elements of the population that he or she feels are most representative of the population. she feels are most representative of the population. The person most knowledgeable on the subject of the The person most knowledgeable on the subject of the study selects elements of the population that he or study selects elements of the population that he or she feels are most representative of the population. she feels are most representative of the population. It is a nonprobability sampling technique. It is a nonprobability sampling technique. Example: A reporter might sample three or four Example: A reporter might sample three or four senators, judging them as reflecting the general senators, judging them as reflecting the general opinion of the senate. opinion of the senate. Example: A reporter might sample three or four Example: A reporter might sample three or four senators, judging them as reflecting the general senators, judging them as reflecting the general opinion of the senate. opinion of the senate.

32 Slide © 2005 Thomson/South-Western Judgment Sampling Advantage: It is a relatively easy way of selecting a Advantage: It is a relatively easy way of selecting a sample. sample. Advantage: It is a relatively easy way of selecting a Advantage: It is a relatively easy way of selecting a sample. sample. Disadvantage: The quality of the sample results Disadvantage: The quality of the sample results depends on the judgment of the person selecting the depends on the judgment of the person selecting the sample. sample. Disadvantage: The quality of the sample results Disadvantage: The quality of the sample results depends on the judgment of the person selecting the depends on the judgment of the person selecting the sample. sample.

33 Slide © 2005 Thomson/South-Western End of Chapter 7, Part B