2. 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

3. 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

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. Finite Population Correction: The finite population correction (fpc) is a correction for overestimation of the variance of a population parameter, e.g., a mean or proportion, when the sample size is 10% or more of the population size.

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.

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

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

8. The Confidence Interval Approach

10. 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 + 1.96 = 182.00 + 1.96(3.18) = 182.00 + 6.23 Thus the 95% confidence interval ranges from $175.77 to $188.23.

11. XLXL _ XUXU _ X _ 0.475 Figure 13.4 95% Confidence Interval

12. Table 13.2 Sample Size Determi nation for Means and Proporti ons

13. 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

14. Figure 13A.1 Finding Probabilities Corresponding to Known Values Area is 0.3413 Area between µ and µ + 1  = 0.3431 Area between µ and µ + 2  = 0.4772 Area between µ and µ + 3  = 0.4986 X Scale

15. Figure 13A.2 Finding Values Corresponding to Known Probabilities Area is 0.500 Area is 0.450 Area is 0.050 X50 X Scale -Z0 Z Scale Figure 13A.2 Finding Values Corresponding to Known Probabilities

16. Figure 13A.3 Finding Values Corresponding to Known Probabilities: Confidence Interval Area is 0.475 X50 X Scale -Z0 Z Scal e Area is 0.025 +Z