Hypothesis Testing

**lpd** · October 13th 2010, 05:35 AM

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...

**CaptainBlack** · October 13th 2010, 06:40 AM

Originally Posted by lpd

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

**lpd** · October 13th 2010, 01:24 PM

don't I have to show that the $\mu \neq \mu_0$ ?

**CaptainBlack** · October 13th 2010, 08:08 PM

Originally Posted by lpd

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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