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Math Help - test statistic and probaility

  1. #1
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    test statistic and probaility

    Assume that
    X1, . . . ,X10 ∼ Normal(μ1, σ1^2) and that Y1, . . . , Y20 ∼ Normal(μ2, σ2^2).

    None of the population parameters are known. Let = μ1 − μ2.

    To test H0 : ≥ 0 versus H1 : < 0 at significance level α = 0.05, we observe samples ~x and ~y.

    (a) What test should be used in this situation?

    If we observe ~x and ~y that result inx = −0.82, s1 = 4.09, y = 1.39, and s2 = 1.22, then what is the value of the test
    statistic?

    (b) If we observe ~x and ~y that result in s1 = 4.09, s2 = 1.22,, and a test statistic
    value of 1.76, then which of the following R expressions best approximates the
    significance probability?

    i. 2*pnorm(-1.76)

    ii. pt(-1.76,df=28)

    iii. pt(1.76,df=10)

    iv. pt(-1.76,df=10)

    v. 2*pt(1.76,df=28)


    (c) True of False: if we observe ~x and ~y that result in a significance probability of p = 0.96, then we should reject the null hypothesis.

    i try to solve this problem ......by using R program

    (a)We should use Welch’s approximate T-test in this situation.

    > v=(((((4.09)^2)/10)+(((1.22)^2)/20))^2)/((((4.09/10)^2)/9)+(((1.22/20)^2)/19))
    > v
    [1] 162.5339
    > qt=qt(.975,v)
    > qt
    [1] 1.974667
    > tw=((-.82-1.39)-0)/(sqrt(((4.09^2)/10)+((1.22^2)/20)))
    > tw
    [1] -1.671927
    ᅵtwᅵ=1.671926<qt=1.974667

    We decline to reject at significance level α=0.05

    (b)
    (ii) pt(-1.76,df=28)

    (c)


    i think i have problem in (a), and (c) please let me know how to solve this problem
    Last edited by mr fantastic; May 3rd 2010 at 06:27 PM. Reason: Increased font size that an STM was not necessary for reading the question. Tried to improve formatting.
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  2. #2
    MHF Contributor matheagle's Avatar
    Joined
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    in part (a) you need to know if you can assume that the two population variances are equal or not
    It seems that you cannot.
    go to http://en.wikipedia.org/wiki/Student's_t-test
    and see where it says Unequal sample sizes, unequal variance
    the unequal variances is the point, not the sample sizes
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