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Math Help - alternative hypotheses

  1. #1
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    alternative hypotheses

    Grades for 2 classes, X and Y

    X:78,89,81,94,60,67,51,73,90,93,81,68,45,100,60,10 2,95,87,85,96,77,79,55,89,86,75,85,76,95,84

    I calculated \bar{x}=79.866667, s^{2}_{x}=216.46 and n=30

    Y:65,95,94,72,56,87,89,28,71,78,54,93,91,68,88,90, 69,78,69,91

    \bar{Y}=76.3, s^{2}_{Y}=293.27 and m=30

    a. test the hypothesis H_{0}: \mu_{X}-\mu_{Y} against the alternative H_{1}: \mu_{X}>\mu_{Y} at the \alpha =0.10 significance level assuming X and Y are N(\mu_{X},\sigma^{2}_{X}) and N(\mu_{Y},\sigma^{2}_{Y}) where \sigma^{2}_{X}=\sigma^{2}_{Y}

    I started by using t=\frac{\bar{X}-\bar{Y}}{S_{p}\sqrt{1/n+1/m}} and critical region t \ge t_{0.10}(48)=1.299

    b. test the hypothesis H_{0}: \sigma^{2}_{X}=\sigma^{2}_{Y} against the alternative hypothesis H_{1}: \sigma^{2}_{X} doesn't = \sigma^{2}_{Y} at the \alpha=10% significance level.

    I started this part with F=\frac{s^{2}_{x}}{s^{2}_{Y}} and F \ge F_{0.05,29,19}=2.04 I don't know how to do this because 29 and 19 are not in the table. If this equality is true though then is H0 rejected?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Here's a F-table that should help.
    http://www.danielsoper.com/statcalc/calc04.aspx
    Also, remember that

    F_{a,b,\alpha}={1\over F_{b,a,1-\alpha}}

    I get (1/0.481414)=2.0772.... using 19,29,.95 in that calculator.
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  3. #3
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    Thats a great tool! if i put in 19, 29 .05, I believe it gives me the F for the 1/F test (\frac{s^{2}_{y}}{s^{2}_{x}}) Does everthing else seem ok to use? All my equations?
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  4. #4
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    Do I have to also include \frac{1}{F}=\frac{s^{2}_{y}}{s^{2}_{x}}=\frac{293.  46}{216.46}=1.3548?

    1.3548 \ge F_{0.05,19,29}=1.93

    Or is only one test sufficient
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