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Math Help - probability of Type I error

  1. #1
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    probability of Type I error

    Calculate the following errors for the following tow cases:

    (a) If the cholesterol level of healthy men is normally distributed with a mean of 180 and a standard deviation of 20, and men with cholesterol levels over 225 are diagnosed as not healthy, what is the probability of a type one error?

    (b) If men predisposed to heart disease have a mean cholesterol level of 300 with a standard deviation of 30, but only men with a cholesterol level over 225 are diagnosed as predisposed to heart disease, what is the probability of a Type II error (null Hypothesis is that a person is not predisposed to heart disease).

    An help on this one would be great!

    thanks
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  2. #2
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    Quote Originally Posted by That Guy View Post
    Calculate the following errors for the following tow cases:

    (a) If the cholesterol level of healthy men is normally distributed with a mean of 180 and a standard deviation of 20, and men with cholesterol levels over 225 are diagnosed as not healthy, what is the probability of a type one error?

    (b) If men predisposed to heart disease have a mean cholesterol level of 300 with a standard deviation of 30, but only men with a cholesterol level over 225 are diagnosed as predisposed to heart disease, what is the probability of a Type II error (null Hypothesis is that a person is not predisposed to heart disease).

    An help on this one would be great!

    thanks
    (a) Calculate \Pr( \text{Reject} \, H_0 \, | \, H_0 \, \text{true}) = \Pr(X > 225 \, | \, X ~ Normal (\mu = 180, \sigma = 20).

    (b) Calculate \Pr( \text{Accept} \, H_0 \, | \, H_0 \, \text{false}) = \Pr(X < 225 \, | \, X ~ Normal (\mu = 300, \sigma = 30).
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