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Chapter 13

Chapter 13. Sampling: Final and Initial Sample-Size Determination. Figure 13.1 Relationship of Sample Size Determination to the Previous Chapters and the Marketing Research Process. Relationship to Previous Chapters. Relationship to Marketing Research Process. Focus of This Chapter.

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Chapter 13

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  1. Chapter 13 Sampling: Final and Initial Sample-Size Determination

  2. Figure 13.1 Relationship of Sample Size Determination to the Previous Chapters and the Marketing Research Process Relationship to Previous Chapters Relationship to Marketing Research Process Focus of This Chapter • Research Design Components (Chapter 3) • Sampling Design Process (Chapter 12) • Statistical Approach to Determining Sample Size • Adjusting the Statistically Determined Sample Size Problem Definition Approach to Problem Research Design Field Work Data Preparation and Analysis Report Preparation and Presentation

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

  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.

  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 Variables Table 13.1 Symbols for Population and Sample Variables

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

  8. The Confidence Interval Approach

  9. The Confidence Interval Approach

  10. 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 + 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. 0.475 0.475 _ _ _ XL X XU Figure 13.4 95% Confidence Interval

  12. Table 13.2 Sample Size Determination for Means and Proportions

  13. Table 13.2 (Cont.) Sample Size Determination for Means and Proportions

  14. 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.

  15. 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 Q1, Q2, Q3, ...QC, each expressed as a proportion, Incidence rate = Q1 x Q2 x Q3....x QC Initial sample size = Final sample size Incidence rate x Completion rate

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

  17. Figure 13A.2Finding Values Corresponding to Known Probabilities Area is 0.500 Area is 0.450 Area is 0.050 X Scale X 50 Z Scale Z = -1.645 0

  18. Figure 13A.3Finding Values Corresponding to Known Probabilities: Confidence Interval Area is 0.475 Area is 0.475 Area is 0.025 Area is 0.025 X Scale X 50 Z Scale Z = 1.96 Z = -1.96 0

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