Which of the following factors is most crucial when

Solution

The appropriate sample size is crucial for ensuring that the results of a study are statistically significant and that the conclusions drawn from the sample can be generalized to the population. One of the most important factors in determining sample size is the desired level of precision and confidence . This involves deciding how close you want your sample's results to reflect the true population parameters and the degree of confidence (e.g., 95% confidence level) that the sample accurately represents the population. A higher level of precision and confidence requires a larger sample size to reduce the margin of error and improve the reliability of the results. Why Other Options Are Wrong : A) Incorrect : The size of the population does not directly determine the sample size. Larger populations do not always require larger samples, especially if the population size is large enough that the sample size stabilizes (i.e., after a certain point, increasing the population size has little effect on the sample size). B) Incorrect : The data collection method influences how data is collected, but it doesn’t directly determine the sample size. D) Incorrect : While resources and time are important considerations, they do not dictate the ideal sample size from a statistical perspective. E) Incorrect : The number of variables involved may affect how the data is analyzed, but it does not directly influence the determination of sample size.