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Thread: Tough t-distribution problem

  1. #1
    Junior Member
    Apr 2009

    Tough t-distribution problem

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  2. #2
    MHF Contributor matheagle's Avatar
    Feb 2009
    $\displaystyle \bar Y-\bar X\sim N(0,9\sigma^2/20)$

    so $\displaystyle {\bar Y-\bar X\over 3\sigma/\sqrt{20}}\sim N(0,1)$

    Both $\displaystyle \bar Y$ and $\displaystyle \bar X$ are independent of $\displaystyle S_X$.

    And $\displaystyle 3S^2_X/\sigma^2\sim\chi^2_3$ or $\displaystyle S^2_X/\sigma^2\sim\chi^2_3/3$.

    Take the square root of this and take the ratio of the normal and the chi-square and you will have your t.
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