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Math Help - Hypotheses testing

  1. #1
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    Hypotheses testing

    I am having trouble with a question that asks: What sample size is needed if the probability of not detecting a change of one standard deviation is to be no more than 1%.
    So the hypotheses is two sides, i.e H0:mu=mu0 and H1: mu is not equal to mu0. So H0 is rejected if |Xbar-mu|>c
    I started by setting the Pr(|Xbar-mu|=1 standard deviation) 0.01 =beta (type 2 error)
    =>Pr(Z=sqrt(n)) 0.01
    => sqrt(n)

    So I am stuck here i know n must be discrete. I am unsure how to proceed, or whether the previous steps I took were correct.
    I would appreciate any help. Thanks in advance.
    Last edited by peruvian; March 5th 2013 at 05:36 PM.
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  2. #2
    MHF Contributor
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    Re: Hypotheses testing

    Hey peruvian.

    I have a feeling you want to find the value of n so that three standard deviations (or standard errors) are in some particular interval.

    For this you need to fix a standard error from your sample (or a standard deviation that is assumed for your population) and solve for n where se/SQRT(n) < 1/3 or 3*se/SQRT(n) < 1.

    A value of 3 gives roughly 99.7% confidence which is what you are looking for as a rough sketch.
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