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A comparison of T test, Z test

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Suppose that we want to estimate the mean cholesterol level in adults aged or more. We choose a random sample of such levels. The random sample we choose has a mean of mg/dL and a standard deviation of mg/dL. For each of the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the population mean.
(In the table, refers to a variable having a standard normal distribution, and refers to a variable having a t distribution.)

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A comparison of different types of hypothesis testing method are included in the answer.

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