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Math Help - Hypothesis Testing

  1. #1
    lpd
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    Hypothesis Testing

    Hi. I have this question I need some help.

    Given a random sample of size n from a normal population with known variance \sigma^2, show that the null hypothesis H_0:\mu = \mu_0 can be tested against the alternative \mu\not=\mu_0 using a one tailed criterion based on the chi-square distribution.

    do I use this? \chi^2 \frac{(n-1)s^2}{\sigma^2}

    I just don't know where to start on this problem...
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by lpd View Post
    Hi. I have this question I need some help.

    Given a random sample of size n from a normal population with known variance \sigma^2, show that the null hypothesis H_0:\mu = \mu_0 can be tested against the alternative \mu\not=\mu_0 using a one tailed criterion based on the chi-square distribution.

    do I use this? \chi^2 \frac{(n-1)s^2}{\sigma^2}

    I just don't know where to start on this problem...
    Under the null hypothesis:

    \displaystyle x= \sum_{i=1}^N \dfrac{(x_i-\mu_0)^2}{\sigma^2}

    has a \chi^2 distribution with $$ N degrees of freedom.

    CB
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  3. #3
    lpd
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    don't I have to show that the  \mu \neq  \mu_0?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by lpd View Post
    don't I have to show that the  \mu \neq  \mu_0?
    That is what you are going to do the hypothesis test to determine.

    In hypothesis testing you assume H_0 and show that under this the value of the test statistic computed from the data lies in the rejection region for H_0

    CB
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