# Chi Square Distribution Problem

1. Mar 5, 2015

### Nexttime35

1. The problem statement, all variables and given/known data
Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)22.
3. The attempt at a solution
I honestly have no idea where to begin with this problem. Any ideas?

2. Mar 5, 2015

### Greg Bernhardt

Tell us what you know about this problem. It must be homework for something you've been learning in class.

3. Mar 5, 2015

### Nexttime35

Well I know that the Sample mean has a normal distribution ~ N(μ,σ2/n), which I think is useful to solve this problem. Now, I am confused about how to use this normal distribution for the sample mean to solve the problem. Any thoughts, using this idea?

4. Mar 5, 2015

5. Mar 5, 2015

### Nexttime35

Hi LCKurtz,

Thanks for the help. I am wondering where you got this equation from? I know it's the z-score, converting the sample mean into the z-score, but how did you come up with the equation? Thanks.

6. Mar 5, 2015

### Nexttime35

Actually I believe I know where this comes from.

the Sum from i=1 to n of Zi2 = the Sum from i=1 to n of ((Xi-μ)/σ)2 = chi square distribution with n degrees of freedom.

7. Mar 5, 2015

### Nexttime35

So, would the distribution of this be N(0,n)?

8. Mar 5, 2015

### LCKurtz

Now you are confusing me. It is your question asking for the distribution of$$\frac {n(\bar X - \mu)^2}{\sigma^2} =\frac{(\bar X - \mu)^2}{(\frac \sigma {\sqrt n})^2}$$
So if $Z = \frac{(\bar X - \mu)}{\frac \sigma {\sqrt n}}$, you know $Z\sim n(0,1)$ and your problem is to find the distribution of $Z^2$.