You have learned that the student’s t-distribution for a population mean is to be used when the population standard deviation is unknown, and the z-score distribution for a population mean when the population standard deviation is known. When creating a confidence interval for a mean, what situations could you imagine it appropriate to use the z-score instead of the t-distribution? Why would you use “z” instead of “t” in those instances? For example: If a teacher knows all their old test scores and wants to find out what percentile their favorite student landed in, they could be justified in using a z-score since they know the population variance of the test scores".
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The sample size is large and the population standard deviation is known. In that case, we can use z instead of t....