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Math Help - test statistic?

  1. #1
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    test statistic?

    X and Y stand for the size of the male and femal of a specific species of moth. Assume the distributions of X and Y are N(\mu_{X},\sigma^{2}_{X}) and N(\mu_{Y},\sigma^{2}_{Y}). \sigma^{2}_{Y}>\sigma^{2}_{X} . Use the modification of Z to test the hypothesis H_{0}: \mu_{X}-\mu_{Y}=0 against the alternative hypothesis H_{1}: \mu_{X}-\mu_{Y}<0.

    How do you define the test statistic and a critical region that has a significance level of \alpha=0.025?

    thank you very much
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  2. #2
    MHF Contributor matheagle's Avatar
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    1 Do you know the population variances?
    If so the rejection region is (-\infty ,-1.96)

    and the test statistic is {\bar X-\bar Y\over \sqrt{ {\sigma^{2}_{Y}\over n_Y}+{\sigma^{2}_{X}\over n_X}}}.

    2 If you don't know \sigma^{2}_{Y} and \sigma^{2}_{X}, then it's a t test.
    BUT now I need to know if you're allowed to assume that \sigma^{2}_{Y}=\sigma^{2}_{X} or not.

    3 HOWEVER, if the sample sizes are large then you can approximate this via the Central Limit Theorem and use 1.
    Last edited by matheagle; June 22nd 2009 at 05:37 PM.
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  3. #3
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    That is all the info I have (and part of why I am so stuck)
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