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# Chapter 14 MARK 302 Notes.docx

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CHAPTER 14SAMPLE SIZE DETERMINATIONDetermining Sample Size for Probability SamplesAs a general rule the larger the sample is the smaller the sampling error However large samples cost more money and the resources available for a project are always limited Although the cost of increasing sample size tends to rise on a linear basis double the sample size almost double the cost sampling error decreases at a rate equal to the square root of the relative increase in sample size If sample size is quadrupled data collection cost is almost quadrupled but the level of sampling error is reduced by only 50Budget Available What sample size can we afford once other project costs are deducted This also includes timeRule of Thumb Is there some convention we can apply What might make an adequate sample size based on past experienceNumber of Subgroups Analyzed In any sample size determination problem consideration must be given to the number and anticipated size of various subgroups of the total sample that must be analyzed The larger the number of subgroups to be analyzed the larger the required total sample sizeTraditional Statistical Methods Variance heterogeneity in the population standard deviation sampling error and confidence intervals play a key role in determining sample sizeDetermining Sample Size for Probability SamplesJudgement Best guess of experts Draw on your experience to determine sample sizeConventional What have others done See what the sample size has been for similar studiesThe Normal DistributionGeneral PropertiesMany variables encountered by marketing have probability distributions that are close to the normal distributionUseful approximation of many other discrete probability distributionsUseful for a number of theoretical reasonsincluding the central limit theoremCentral Limit Theorem The idea that a distribution of a large number of sample means or sample proportions will approximate a normal distributionregardless of the distribution of the population from which they were drawnCharacteristics of a Normal Distribution1The continuous distribution that is bell shaped and symmetrical about the mean2The mean median and mode are equal

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