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Determining Sample Size Variable Population Sample Mean μ Proportion π p Standard deviation σ s Size N n Variance Standard error of the mean Standard error of the proportion Standardized variate (z) Copyright © 2012 Pearson Education, Inc. Chapter 13 -2 Confidence Interval Approach Means Copyright © 2012 Pearson Education, Inc. Proportions Chapter 13 - 3 The Confidence Interval Approach z . Chapter 13 - 4 Copyright © 2012 Pearson Education, Inc. The Confidence Interval Approach (Cont.) Copyright © 2012 Pearson Education, Inc. Chapter 13 - 5 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 = 182.00 + 1.96(3.18) = 182.00 + 6.23 Thus the 95% confidence interval ranges from $175.77 to $188.23. Copyright © 2012 Pearson Education, Inc. Chapter 13 - 6 0.475 Copyright © 2012 Pearson Education, Inc. 0.475 Chapter 13 - 7 Steps Means Proportions 2. Specify the confidence level (CL). CL = 95% CL = 95% 3. Determine the z value associated with the CL. Z value is 1.96 Z value is 1.96 1. Specify the level of precision. Copyright © 2012 Pearson Education, Inc. Chapter 13 - 8 Steps 4. Determine the standard deviation of the population Means Proportions Estimate σ σ = 55 Estimate π π = 0.64 5. Determine the sample size using the formula for the standard error 6. If necessary, reestimate the confidence interval by employing s to estimate σ Copyright © 2012 Pearson Education, Inc. Chapter 13 -9 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 Copyright © 2012 Pearson Education, Inc. Chapter 13 - 10 International Marketing Research • When conducting marketing research in foreign countries, statistical estimation of sample size can be difficult, because estimates of the population variance might be unavailable. • When statistical estimation of sample size is attempted, the differences in estimates of population variance should be recognized and factored in, if possible. • When the goal is to examine differences across countries or international markets, it is desirable to have the same sample size across countries. Copyright © 2012 Pearson Education, Inc. Chapter 13 - 11