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# day20 - Hypothesis Tests for Unknown In the last section we...

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Hypothesis Tests for μ - Unknown σ In the last section, we learned how to perform hypothesis tests for the popu- lation mean when the population standard deviation is a known value. Now, we show how to perform hypothesis tests when the population standard de- viation is not known. We use the sample standard deviation s to estimate the population stan- dard deviation σ . The test statistic is now t = ¯ x - μ 0 s/ n The distribution of the test statistic now follows a t distribution with ( n - 1) degrees of freedom. The procedure is the same as the procedure for the known σ case, but p -values and critical values are computed using the t distribution with ( n - 1) degrees of freedom. 1

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One-Tailed Test Example : The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of \$238 per week. A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level.
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day20 - Hypothesis Tests for Unknown In the last section we...

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