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Lecture Business research methods (12/e): Chapter 14A - Donald R. Cooper, Pamela S. Schindler

Chapter 14A - Determining sample size. This chapter presents the following content: Random samples, increasing precision, confidence levels & the normal curve, standard errors, central limit theorem, estimates of dining visits, calculating sample size for questions involving means,. | Determining Sample Size Appendix 14a McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Random Samples 2 Exhibit 14a-1 shows the Metro U dining club study population (N = 20,000) consisting of five subgroups based on their preferred lunch times. The values 1 through 5 represent preferred lunch times, each a 30-minute interval, starting at 11:00 a.m. Next we sample 10 elements from this population without knowledge of the population’s characteristics. We draw four samples of 10 elements each. The means for each sample are provided in the slide. Each mean is a point estimate, the best predictor of the unknown population mean. None of the samples shown is a perfect duplication because no sample perfectly replicates its population. We cannot judge which estimate is the true mean of the population but we can estimate the interval in which the true mean will fall by using any of the samples. This is accomplished by using a formula that computes the | Determining Sample Size Appendix 14a McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Random Samples 2 Exhibit 14a-1 shows the Metro U dining club study population (N = 20,000) consisting of five subgroups based on their preferred lunch times. The values 1 through 5 represent preferred lunch times, each a 30-minute interval, starting at 11:00 a.m. Next we sample 10 elements from this population without knowledge of the population’s characteristics. We draw four samples of 10 elements each. The means for each sample are provided in the slide. Each mean is a point estimate, the best predictor of the unknown population mean. None of the samples shown is a perfect duplication because no sample perfectly replicates its population. We cannot judge which estimate is the true mean of the population but we can estimate the interval in which the true mean will fall by using any of the samples. This is accomplished by using a formula that computes the standard error of the mean. Increasing Precision 3 Exhibit 14a-2 The standard error creates an interval estimate that brackets the point estimate. The interval estimate is an interval or range of values within which the true population parameter is expected to fall. In this example, mu is predicted o be 3.0 or 12:00 noon plus or minus .36. Thus we would expect to find the true population parameter to be between 11:49 a.m. and 12:11 p.m. We have 68% confidence in this estimate because one standard error encompasses plus or minus 1 Z. This is illustrated in Exhibit 14a-3 on the next slide. Confidence Levels & the Normal Curve 4 Exhibit 14a-3 The area under the curve represents the confidence estimates that one makes about the results. The combination of the interval range and the degree of confidence creates the confidence interval. With 95% confidence, the interval in which we would find the true mean increases from 11:39 a.m. to 12:21 p.m. We find this by multiplying the standard error