# Factors Affecting Sample Size: Problem Set

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1. There are several factors that affect the sample size estimate for a study. These the population size, the confidence interval and the confidence level. The population size is important because the sample size must be sufficiently large that the results can be extrapolated to the population at large. This will not be the case if the sample size is too small (CRS, 2012). In addition to the population size, the confidence level and interval will also factor into the sample size. The greater the degree of confidence that the researcher wants to have in the results, the larger the sample size needs to be. The confidence level is a measure of how certain the results are. This is typically 95% or 99%, but any number can be chosen. 95% is typical (Ibid). The confidence interval is a plus or minus value that is attached to the result. Thus, a result that is 50% of respondents with a 99% level and a 3% interval would mean that the researcher is 99% certain that the result is going to be between 47-53%. 2. The sample size is estimated using a formula that takes into account these different factors. . There are sample size calculators online. The sample size formula is: ss = Z 2 * (p) * (1-p) c 2 The above is for an infinite population. With a finite population: ss new ss = 1+ ss-1 pop In the first formula, the Z value relates to the confidence level, so 1.96 reflects a confidence level of 95. A contingency table is a matrix that shows the