Final answer:
The question involves a statistical method for determining the required sample size for a study, based on the desired confidence level, margin of error, and an estimate of population proportions. Using the formula involving the Z-score, margin of error, and population proportions, one can calculate the necessary sample size to ensure enough precision in the study's findings.
Step-by-step explanation:
The question refers to the sampling methodology used in statistics to determine the sample size (n) required for a study. To calculate the sample size n, the formula n = (Z²×p'q')/(EBM²) is used, where Z is the critical value that corresponds to the desired confidence level (Cl), p' is the estimated proportion of the population that has a particular characteristic, q' is 1-p (the proportion that does not have the characteristic), and EBM stands for the desired margin of error. Researchers round up the calculated sample size to ensure it is large enough to maintain the desired confidence level and margin of error. Increasing the sample size beyond 100 is known to decrease the margin of error.
In practical settings, if a researcher knows the standard deviation (σ) of a population and the desired EBM, they can substitute these values into the formula along with the Z-score for their confidence level to find the required sample size. For example, using a standard deviation of 15, an EBM of 2, and a confidence level of 95% (which corresponds to a Z-score of 1.96), the formula would yield a n of 217, which is then rounded up to ensure the sample is large enough.