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Math Help - very last doubt

  1. #1
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    very last doubt

    I have a doubt over the way my teacher solved this exercice:

    Let X be a Normal random variable N (μ, σ2= 169) with an unknown parameter μ. For testing the
    hypothesis H0: μ = 28 versus H1: μ = 31 a random sample of size n = 225 is observed.
    a) Consider the following rejection region: ( ){ }1107,29:...,, 2251 ≥≡ xxxR . Evaluate α (the
    probability of the type I error) and β (the probability of the type II error) corresponding to the given
    test.
    b) Calculate the p-value corresponding to the following sample:

    (32, 29, 28, 34, 27)

    For the point b) my teacher wrote P[Z>=(30-28)/(13/15)]
    I do not understand why she used 15 when the new sample is 5 ?
    Thank you.
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  2. #2
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    I just realize the text did not appear properly: here is the correct:

    Let X be a Normal random variable N (μ, σ2= 169) with an unknown parameter μ. For testing the hypothesis H0: μ = 28 versus H1: μ = 31 a random sample of size n = 225 is observed.
    a) Consider the following rejection region: RX_mean>= 29.1107) evaluate the probability alpha of the type I error(reject H_0 when H_0 true) and β (the probability of the type II error= accept H_0 when H_0 false) corresponding to the given test.
    b) Calculate the p-value corresponding to the following sample:

    (32, 29, 28, 34, 27)

    Point a) is okay.
    For the point b) my teacher wrote P[Z>=(30-28)/(13/15)]
    I do not understand why she used 15 when the new sample is 5 ?
    Thank you.

    Please help. Exam tomorrow.
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  3. #3
    GAMMA Mathematics
    colby2152's Avatar
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    I'm not sure where you are getting a sample size of five. The sample size is n=225, so \sqrt{n} = 15
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  4. #4
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    Quote Originally Posted by colby2152 View Post
    I'm not sure where you are getting a sample size of five. The sample size is n=225, so \sqrt{n} = 15
    Because it says:

    Calculate the p-value corresponding to the following sample:

    (32, 29, 28, 34, 27)
    which are 5.
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  5. #5
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    Quote Originally Posted by 0123 View Post
    I have a doubt over the way my teacher solved this exercice:

    Let X be a Normal random variable N (μ, σ2= 169) with an unknown parameter μ. For testing the
    hypothesis H0: μ = 28 versus H1: μ = 31 a random sample of size n = 225 is observed.
    [snip]
    b) Calculate the p-value corresponding to the following sample:

    (32, 29, 28, 34, 27)

    For the point b) my teacher wrote P[Z>=(30-28)/(13/15)]
    I do not understand why she used 15 when the new sample is 5 ?
    Thank you.
    You're right, clearly n = 5.
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  6. #6
    GAMMA Mathematics
    colby2152's Avatar
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    Quote Originally Posted by 0123 View Post
    Because it says:

    Calculate the p-value corresponding to the following sample:

    (32, 29, 28, 34, 27)
    which are 5.
    I must have missed that. The new sample size is 5 rather than 225 as Mr. Fantastic pointed out.
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