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Math Help - Null Hypothesis

  1. #1
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    Question Null Hypothesis

    A precision instrument is guaranteed to read accurately to within 2 units. A sample of 4 instrument readings on the same object yielded the measurements 353, 351, 351, and 355. Test the null hypothesis that σ=0.7 against the alternative σ >0.7. Use alpha=0.05.

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  2. #2
    MHF Contributor matheagle's Avatar
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     H_0:\sigma=.7 vs.  H_a:\sigma>.7

    the test stat is  {(n-1)S^2\over \sigma^2_0} ={\sum_{i=1}^4(X_i-\bar X)^2\over .49}

    However it's easier to get the sample variance for {1,1,3,5}.
    I did that by subtracting 350 from each.

    Hence our test stat is  {(n-1)S^2\over \sigma^2_0} ={11\over .49}\approx 22.449

    The rejection region is based on a  \chi^2 with 3 degrees of freedom
    giving us the interval  (7.815,\infty )

    You should at this level (alpha) reject the null hypothesis and accept the alternative hypothesis.
    Last edited by matheagle; November 24th 2009 at 12:54 AM.
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