1. ## Hypothesis Testing

Hi. I have this question I need some help.

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

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

I just don't know where to start on this problem...

2. Originally Posted by lpd
Hi. I have this question I need some help.

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

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

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

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

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

CB

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

4. Originally Posted by lpd
don't I have to show that the $\displaystyle \mu \neq \mu_0$?
That is what you are going to do the hypothesis test to determine.

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

CB