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Thank you for your post and sharing the information you found about z-scores and t-statistics. It seems clear that z-scores are using in situations where the population information is known and it is necessary to make a determination about the sample. A larger sample size, up to 30, helps make the distribution normal if it isn't already, and generally speaking, the larger the sample size, the more sensitive the test is to showing a significant effect. The same is true for the t-statistic, except that it represents an estimation of the difference between the sample means and the population mean by using the sample variance to compute an estimated standard error. As with the z-score, the larger the sample size, and more likely it is that a significant effect can be detected.