Determining Sample Size Each slide has its own narration in an audio file. For the explanation of any slide click on the audio icon to start it. Professor Friedman's Statistics Course by H & L Friedman is licensed under a  Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. 

Sample Size Determination: µ In estimating µ based on sample statistics, how large a sample do we need for the level of precision we want? To determine the sample size we need, we must know the (1) desired precision and (2) σ. e, the half-width of the confidence interval estimator is the precision with which we are estimating. e is also called sampling error. Sample Size Determination

Sample Size Determination: µ …continued We use e to solve for n: If then and so Sample Size Determination

Example Suppose σ=20 based upon previous studies. We would like to estimate the population mean within ±10 of its true value, at α=.05 (i.e., 95% confidence). What sample size should we take? = 15.4 so, we need a sample size of at least 15.4, or n=16. We round UP, not down. Sample Size Determination

Sample Size Determination: P Similarly, taking e (precision) from formula for the half-width of a confidence interval estimator for P: Q: If we are trying to estimate the population proportion, P, what do we use for P in this formula? Sample Size Determination

Example: Political Poll Suppose a pollster wants a maximum error of e = .01 with 95% confidence. We assume that variance is the highest possible, so we use P=.5. This is the way we ensure that sampling error will be within ±.01 of the true population Proportion.   Then, n = = 9,604 That is a VERY large sample. Sample Size Determination

Example: Political Poll …continued Let’s try that again with e = .03.   n = = 1,067 This is the sample size that most pollsters work with. Sample Size Determination

Homework Practice, practice, practice. As always, do lots and lots of problems. You can find these in the online lecture notes and homework assignments. Sample Size Determination