Thread: test statistics/critical regions
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Old June 24th, 2009, 09:06 PM
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a) The test statistic is T = \frac {\bar{X} - \bar{Y}}{S_{p} \sqrt{1/n + 1/m}}

where S_{p} = \sqrt{\frac{(n-1)S^{2}_{X} + (m-1)S^{2}_{Y}}{n+m-2}}

T follows a t distribution with n+m-2 degrees of freedom

For this problem the critical region is t \ge t_{(0.01, 27)}


c) The alternative hypothesis is H_{1}: \sigma^{2}_{X} \neq \sigma^{2}_{Y}

The test statistic is F = \frac {S^{2}_{X}}{S^{2}_{Y}}

F follows an F distribution with r_{1} = n-1 and r_{2}=m-1 degrees of freedom respectively

The critical region is f \ge F_{(0.025, 15,12)} or \frac {1}{f} \ge F_{(0.025,12,15)}


I have to review how to do part (d).
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