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    October 10, 2022

Comment 1
Z-tests are used to compare the collected data of a defined population and the sample.  The z-score tells you how far, in standard deviation, a data point is from the mean or average of a data set. A z-test compares a sample to a defined population. Normally, a z-test identifies issues with larger samples that are being studied (n > 30). Z-tests are also useful when testing out a hypothesis. Generally, they are most useful when the standard deviation is known.
T-tests are calculations used to test a hypothesis. However, t-tests are used to determine the statistical difference between two independent sample groups. In other words, a t-test analyzes how likely the difference between two samples occurs due to random chance. Usually, t-tests are most appropriate to use when dealing with problems with a limited or small sample size (n 30 n>30 (due to CLT)
2. Population binomial,  n p > 10 np>10,   n q >10 nq>10
You use the   t- score test if:
1. Population normal, variance unknown and   n < 30 n<30
2. No knowledge about population or variance and   n < 30 n<30, but sample data looks normal / passes tests etc. so population can be assumed normal.

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