© 2009 Pearson Education, Inc publishing as Prentice Hall 13-1 Chapter 13 Sampling: Final and Initial Sample-Size Determination

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-2 Figure 13.1 Relationship of Sample Size Determination to the Previous Chapters and the Marketing Research Process Focus of This Chapter Relationship to Previous Chapters Relationship to Marketing Research Process Statistical Approach to Determining Sample Size Adjusting the Statistically Determined Sample Size Research Design Components (Chapter 3) Sampling Design Process (Chapter 12) Problem Definition Approach to Problem Field Work Data Preparation and Analysis Report Preparation and Presentation Research Design

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-3 Application to Contemporary Issues (Fig 13.5) TechnologyEthicsInternational Be a DM! Be an MR! Experiential Learning Opening Vignette What Would You Do? Definitions and Symbols The Sampling Distribution Statistical Approach to Determining Sample Size Confidence Interval Approach Adjusting the Statistically Determined Sample Size Figs 13a.1-13a.3 Fig 13.3 Fig 13.4 Table 13.2 Appendix 13a Table 13.1 Figure 13.2 Final and Initial Sample Size Determination: An Overview Means Proportions

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-4 Definitions and Symbols Parameter: A parameter is a summary description of a fixed characteristic or measure of the target population. A parameter denotes the true value which would be obtained if a census rather than a sample was undertaken. Statistic: A statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter. Random sampling error: The error when the sample selected is an imperfect representation of the population of interest.

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-5 Definitions and Symbols Precision level: When estimating a population parameter by using a sample statistic, the precision level is the desired size of the estimating interval. This is the maximum permissible difference between the sample statistic and the population parameter. Confidence interval: The confidence interval is the range into which the true population parameter will fall, assuming a given level of confidence. Confidence level: The confidence level is the probability that a confidence interval will include the population parameter.

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-6 Table 13.1 Symbols for Population and Sample VariablesTable 13.1 Symbols for Population and Sample Variables Table 13.1 Symbols for Population and Sample Variables

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-7 Figure 13.3 The Confidence Interval Approach and Determining Sample Size Confidence Interval Approach MeansProportions

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-8 The Confidence Interval Approach

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-9 The Confidence Interval Approach

© 2009 Pearson Education, Inc publishing as Prentice Hall The Confidence Interval Approach The confidence interval is given by We can now set a 95% confidence interval around the sample mean of $182. The 95% confidence interval is given by = (3.18) = Thus the 95% confidence interval ranges from $ to $

© 2009 Pearson Education, Inc publishing as Prentice Hall XLXL _ XUXU _ X _ Figure % Confidence Interval

© 2009 Pearson Education, Inc publishing as Prentice Hall Table 13.2 Sample Size Determination for Means and Proportions

© 2009 Pearson Education, Inc publishing as Prentice Hall Table 13.2 (Cont.) Sample Size Determination for Means and Proportions

© 2009 Pearson Education, Inc publishing as Prentice Hall A sample size of 400 is enough to represent China’s more than 1.3 billion people or the more than 300 million American people. The sample size is independent of the population size for large populations.

© 2009 Pearson Education, Inc publishing as Prentice Hall Adjusting the Statistically Determined Sample Size Incidence rate refers to the rate of occurrence or the percentage of persons eligible to participate in the study. In general, if there are c qualifying factors with an incidence of Q 1, Q 2, Q 3,...Q C, each expressed as a proportion, Incidence rate= Q 1 x Q 2 x Q 3....x Q C Initial sample size= Final sample size Incidence rate x Completion rate

© 2009 Pearson Education, Inc publishing as Prentice Hall 13-16

© 2009 Pearson Education, Inc publishing as Prentice Hall Figure 13A.1 Finding Probabilities Corresponding to Known Values Area is Area between µ and µ + 1  = Area between µ and µ + 2  = Area between µ and µ + 3  = X Scale

© 2009 Pearson Education, Inc publishing as Prentice Hall Figure 13A.2 Finding Values Corresponding to Known Probabilities Area is Area is Area is X50 X Scale Z = Z Scale

© 2009 Pearson Education, Inc publishing as Prentice Hall Figure 13A.3 Finding Values Corresponding to Known Probabilities: Confidence Interval Area is X50 X Scale Z = Z Scal e Area is Z = 1.96