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Thread: Type I and Type II Error

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    Type I and Type II Error




    Let {X1, X2, ..., X25} be a random sample of 25 observations from a normal population havingmean μ and variance 2. Define the null hypothesis H0 : μ = 0 and the alternative hypothesisH1 : μ > 0. Consider the following decision rule:
    reject H0 if X' > 0.5accept H0 if X' ≤ 0.5
    a.) Calculate the probability of making a type I error.
    b.) Calculate the probability of making a type II error when in fact μ = 0.2.


    what I got till now is
    z=(X'-)(𝛔/sqrt(n))
    z=.5/sqrt(2)
    X'=z*(Sqrt(2/25))+0
    .... any ideas ???

    thank you so much

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    Re: Type I and Type II Error

    Quote Originally Posted by oharman View Post
    what I got till now is
    z=(X'-)(��/sqrt(n))
    z=.5/sqrt(2)
    X'=z*(Sqrt(2/25))+0
    .... any ideas ???

    thank you so much

    I can't quite make out your response. However, you know what your level of significance is (>0.05), so you should be able to incorporate that into your equation.
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    Re: Type I and Type II Error

    the level of significance is not given?? I could however assume 0.05 but then there is no room left for a calculation of type I error...since If I impose lvl sign I indirectly set alpha ???

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    Re: Type I and Type II Error


    Quote Originally Posted by hlsmith View Post
    However, you know what your level of significance is (>0.05), so you should be able to incorporate that into your equation.
    Ignore this (sorry hlsmith).

    You're given the cutoff and asked to determine the type I error rate (the "level of significance").
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