If the population standard deviation is available and the sample size is greater than 30, t-distribution can be used with the population standard deviation instead of the sample standard deviation. Summary: If the sample sizes are larger than 30, the z-distribution and the t-distributions are pretty much the same and either one can be used. The t-score is calculated using the formula: T-Score tells you how many standard deviations from the mean your result is. t-statistics (t-score), also known as Student's T-Distribution, is used when the data follows a normal distribution, population standard deviation ( sigma) is NOT known, but the sample standard deviation ( s) is known or can be calculated, and the sample size is below 30.The z-score is calculated using the formula: Z-Score tells you how many standard deviations from the mean your result is. z-statistics (z-score) is used when the data follows a normal distribution, population standard deviation sigma is known and the sample size is above 30.If you are interested in T-test, you can do similar: Finding the proportion of a normal distribution that is above a value by calculating a z-score and using a z-table.
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