Tests concerning a population mean

Tests concerning a population mean - Tests concerning a...

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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=n-1 degrees of freedom is the test statistic.
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Cases 1 and 2: The Distribution of the Test Statistic, Alternative Hypotheses and Rejection Regions for : Alternative Hypothesis Rejection Region Standard Normal Distribution
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Alpha is The probabilityof rejecting the null hypothesis when it is true . Commonly Chosen Values for α , Standard Normal Percentiles and Critical Values α .05 .025 .01 .005 1 - α .95 .975 .99 .995 Percentiles 95 97.7 99 99.5 Critical Values = qnorm( 1 α) 1.645 1.96 2.33 2.58
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Example Question with the Statistics Given The
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