Re: Statistics - Chi-Square

If anyone can help with this problem, it would be really appreciated.

Re: Statistics - Chi-Square

a) $X1^2+X2^2+X3^2$ is chi square with 3 degrees of freedom... just from the first line of the wiki definition

b) $X1^2, X2^2, X3^2$ are all chi squared with 1 degree of freedom. $X1^2+X2^2$ for example is chi square w/2 degrees of freedom.

so $ \dfrac{X1^2}{\dfrac{X2^2+X3^2}{2}}$ is F distributed with 1 and 2 degrees of freedom

c) it looks like if you let $\overline{X}=\dfrac{X1+X2+X3}{3}$ then

$\dfrac{\overline{X}-i}{ \dfrac{i^2}{ \sqrt{3}}}$ is t distributed with 2 degrees of freedom

reading up on the t statistic makes me think it's how you answer that question about the machines being adjusted properly