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Math Help - 'Universal' Formula for finding the probablilty of a Type 1 Error

  1. #1
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    'Universal' Formula for finding the probablilty of a Type 1 Error

    Hi!
    I'm an AP stats student and I'm fortunate enough to have an EXTREMELY incompetent teacher (a bit of sarcasm there) so I was wondering if anyone could properly explain how to find the probability of getting a Type 1 Error... this seems to be an area that few text books explain thoroughly... although mine explains how to find a Type 2 quite thoroughly. Go figure.

    If anyone even has time to write only the formula that would be more than enough!!

    Thanks!!
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  2. #2
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    Quote Originally Posted by agoelz13 View Post
    Hi!
    I'm an AP stats student and I'm fortunate enough to have an EXTREMELY incompetent teacher (a bit of sarcasm there) so I was wondering if anyone could properly explain how to find the probability of getting a Type 1 Error... this seems to be an area that few text books explain thoroughly... although mine explains how to find a Type 2 quite thoroughly. Go figure.

    If anyone even has time to write only the formula that would be more than enough!!

    Thanks!!
    This is the formula: Pr(reject H0 | H0 true).

    The best way is to read examples like this one: http://www.mathhelpforum.com/math-he...e-i-error.html

    I'm sure a search of these forums will uncover other examples.
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    Umm... ok I think I need the in-depth explanation because unfortunately that formula as well as the other examples I've found aren't making sense to me... perhaps it would be easier to explain with a problem?:

    You have an SRS of size n= 9 from a normal distribution with \sigma = 1. You wish to test

    \, H_O \,: \mu = 0<br />

    \, H_O\,: \mu > 0<br />

    You decide to reject \,H_O\, if \bar{x} > 0 and to accept \,H_O\, otherwise.

    (a) Find the probability of a type 1 error

    (b) Find the probability of a type 2 error when \mu = 0.3

    (c) Find the probability of a type 2 error when \mu = 1
    Last edited by agoelz13; February 18th 2009 at 10:30 PM.
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    Quote Originally Posted by agoelz13 View Post
    Umm... ok I think I need the in-depth explanation because unfortunately that formula as well as the other examples I've found aren't making sense to me... perhaps it would be easier to explain with a problem?:

    You have an SRS of size n= 9 from a normal distribution with \sigma = 1. You wish to test

    \, H_O \,: \mu = 0<br />

    \, H_O\,: \mu > 0<br />

    You decide to reject \,H_O\, if \bar{x} > 0 and to accept \,H_O\, otherwise.

    (a) Find the probability of a type 1 error

    (b) Find the probability of a type 2 error when \mu = 0.3

    (c) Find the probability of a type 2 error when \mu = 1
    (a) Calculate \Pr( \text{Reject} \, H_0 \, | \, H_0 \, \text{true}) = \Pr\left(\overline{X} > 0 {\color{white}\frac{.}{.}} | \, \overline{X}\right. ~ Normal \left.\left(\mu = 0, \sigma = \frac{1}{\sqrt{9}}\right)\right).
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