Determining Sample Size
In the business world, sample sizes are determined prior to data collection to ensure that the confidence interval is narrow enough to be useful in making decisions. Determining the proper sample size is a complicated procedure, subject to the constraints of budget, time, and the amount of acceptable sampling error. If you want to estimate the mean dollar amount of the sales invoices, you must determine in advance how large a sampling error to allow in estimating the population mean. You must also determine, in advance, the level of confidence (i.e., 90%, 95%, or 99%) to use in estimating the population parameter.
The sampling error, e, is defined as Solving for n gives the sample size needed to construct the appropriate confidence interval estimate for the mean. “Appropriate” means that the resulting interval will have an acceptable amount of sampling error. To compute the sample size, you must know three factors:
The desired confidence level, which determines the value of the critical value from the standardized normal distribution •
The acceptable sampling error
The standard deviation
In some business-to-business relationships that require estimation of important parameters, legal contracts specify acceptable levels of sampling error and the confidence level required. For companies in the food and drug sectors, government regulations often specify sampling errors and confidence levels.
In general, however, it is usually not easy to specify the three factors needed to determine the sample size. How can you determine the level of confidence and sampling error? Typically, these questions are answered only by a subject matter expert (i.e., an individual very familiar with the variables under study). Although 95% is the most common confidence level used, if more confidence is desired, then 99% might be more appropriate; if less confidence is deemed acceptable, then 90% might be used. For the sampling error, you should...
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