OPENING QUESTIONS 1.What key concepts and symbols are pertinent to sampling? 2.How are the sampling distribution, statistical inference, and standard error relevant to sampling? 3.What is the statistical approach to determining sample size based on simple random sampling and the construction of confidence intervals? 4.How can we derive the formulas to statistically determine the sample size for estimating means and proportions? 5.How should the sample size be adjusted to account for incidence and completion rates? 6.Why is it difficult to statistically determine the sample size in international marketing research? 7.What is the interface of technology with sample size determination? 8.What ethical issues are related to sample size determination, particularly the estimation of population variance?

Figure 13.1 Relationship to the Previous Chapters & The Marketing Research Process 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

Application to Contemporary Issues 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

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. Sampling Distribution: A distribution of the values of a sample statistic, for example, the sample mean.

Definitions and Symbols Central Limit Theorem: as the sample size increases, the distribution of the sample mean of a randomly selected sample approaches normal 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.

Table 13.1 Symbols for Population and Sample VariablesTable 13.1 Symbols for Population and Sample Variables

Figure 13.3 The Confidence Interval Approach and Determining Sample Size Confidence Interval Approach MeansProportions

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 $

XLXL _ XUXU _ X _ Figure % Confidence Interval

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

Figure 13A.2 Finding Values Corresponding to Known Probabilities Area is Area is Area is X50 X Scale -Z0 Z Scale Figure 13A.2 Finding Values Corresponding to Known Probabilities

Figure 13A.3 Finding Values Corresponding to Known Probabilities: Confidence Interval Area is X50 X Scale -Z0 Z Scal e Area is Z