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Math Help - the probability of making a type II error CALCULATE BETA

  1. #1
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    the probability of making a type II error CALCULATE BETA

    You draw one observation from a normal distribution with known variance 1. You want to test if mu = 0.
    a) Find c such that if you reject H0 when |x| > c, you get alfa to be 0.05.
    b) With this rejection region, calculate beta (the probability of making a type II error) if the true value of mu is 0.2,
    Answer in the form 3.54,0.64 using 2 decimals.


    please help, don't understand without n ?

    Thanks in advance
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  2. #2
    MHF Contributor matheagle's Avatar
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    First of all, since you are rejecting the null with alpha=.05 the rejection region is

    (-\infty,-1.96)\cup (1.96,\infty)

    since .05=P(|X|>1.96)

    Now, \beta=P(-1.96<X<1.96) when the MOO is .2 and variance is 1.

    so you need to standardize appropriately...

    \beta=P(-1.96<X<1.96)=P(-1.96-.2<X-.2<1.96-.2)

    =P(-2.16<Z<1.76)

    I don't know what this '3.54,0.64' is
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