Hi Professor,
Your summary of the 3-facts is well outlined, helping to improve the understanding of the central limit theorem, even for a person not skilled in statistics. Very impressive. I support your evaluation and final comment on the importance of the central limit theorem as a tool in predicting the population. As a researcher, this is a valuable tool, especially when one cannot fully access the whole population.
However, in attaining normality, a critical condition is essential, which is a large enough sample size, e.g., no less than 30 units (Bowerman, Murphree & O’Connell, 2015). Also, that is large enough. This means as a business or health researcher, there is a need to adopt other exploratory techniques in determining the right sample for utilization across different arising situations. This is because one case might only need just 30 samples, while another might need 150, and another 450. Nevertheless, the central limit theorem is an essential tool, applicable across multiple situations, e.g., politics, healthcare.
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I appreciate your valuable insights on my discussion and happy to have read your personal and fact-based debate on the central limit theorem. Of all the focus issues, the central limit theorem emerges as an essential tool, allowing in summarizing information about the population. In typical situations, sometimes, it isn’t easy to investigate the whole population, which makes the theorem so important. And as explained by Bowerman, Murphree, and O’Connell (2015), past studies have shown an approximately sample size of 30 attains normal distribution. I agree with your comment on the repetition or largeness of sample size as a critical aspect in making quality inferences, which is adopted in the central limit theorem. By repeating experiments or observations, there is an evident sample that means depicting normality. Hence, as a researcher, with the constraints of time and sometimes data collection finances, sampling and adopting the central limit theorem can be of great help. I plan on applying this theory, not only in this course but also in my future research, as a tool in making accurate predictions about populations.