# Chi sqaure & confidence interval

1. Jun 19, 2008

### sstudent

Lets say you have 5 trials, and 5 output lets say {5, 43, 60, 30 , 4}....so how would u get the chi sqaure from here & the confidence interval. i havent work on prob &statc in years, thanks a lot for help folks

2. Jun 19, 2008

### konthelion

I'm supposing you made up this problem... for your random sample of size n=5 is {5, 43, 60, 30 , 4},these are your observed cells/frequencies, but you do not have have your expected cells/frequencies.

3. Jun 19, 2008

### sstudent

Basically u can do the confidence for 99%

4. Jun 19, 2008

### konthelion

I don't understand what you're trying to do.

For a Chi-Squared test, you need a null hypothesis and alternative hypothesis.
The test statistical value is $$\chi^2=\sum \frac{(O-E)^2}{E}$$
where O is a shorthand notation for your observed cells and E is the shorthand notation for expected cell/frequency.

If you are trying to find the confidence interval for the true variance $$\sigma^2$$, then the formula for that is

$$P\left( C_{1}< \frac{(n-1)s^2}{\sigma^2} < C_{2} \right) = 1- \alpha$$ = .99 since 100(1-alpha)% =99%

where $$C_{1}=\frac{(n-1)s^2}{\chi_{\alpha/2,n-1}}$$ is the lower limit
and
$$C_2 = \frac{(n-1)s^2}{\chi_{1-\alpha/2,n-1}}$$ is your upper limit.

Last edited: Jun 19, 2008
5. Jun 22, 2008

### sstudent

lets say u consider #5 as the thresh#, and for the numbers> 5, u tryto find the confiendnce interval for 99.99% or greater. thanks