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Unformatted text preview: Tests concerning a population mean. The mean of a random sample from a population provides a foundation for creating a test statistic to assesses hypothesis about a population mean . Case 1. The population is from the normal family with mean The standard deviation is known. has a standard normal distribution . is the test statistic. Case 2. The population is from an unknown family with mean The random sample is large (n > 40 rule of thumb). Generally justified by the Central Limit Theorem has approximately a standard normal distribution. is the test statistic. Case 3. The population is from the normal family with mean . The sample size can be small but at least 2. has a t distribution with df=n1 degrees of freedom is the test statistic. Cases 1 and 2: The Distribution of the Test Statistic, Alternative Hypotheses and Rejection Regions for : Alternative Hypothesis Rejection Region Standard Normal Distribution Alpha is The probabilityof rejecting the null hypothesis when it is true ....
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 Spring '08
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