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in this video were going to talk about how to calculate the sample size were going to work on two example problems lets start with this one the average test score of all students in a certain class was measured to be 84 with a standard deviation of 15. if the margin of error was calculated to be 5.367 at a 95 confidence level how many students were in this class well lets write down what we know so the average in this case the mean is 84. the standard deviation is 15. the margin of error is 5.367 and our goal is to calculate the sample size or the number of students that were in this class so how can we do this well it helps to know the formula for the margin of error the margin of error is equal to the z-score times the standard deviation divided by the square root of the sample size if we square both sides well get e squared is equal to z squared times theta squared over n and then if we swap n and e squared we get this formula the sample size is equal to the z is equal to the