## The F distribution

Hey mathematicians.

I have an assignment where i have a table of the air pollution in melbourne and houston.

City.......................USS...................S ..........n

1. Melbourne.........76951,65............947,7....... 13

2. Houston..........118811,59...........1307,2......1 6

They are both normal-distributed (or however you say that.)

$x_{ij} \sim \sim N(\mu_{i},\sigma_{i}^{2}), \hspace{10 mm} i=1,2 \hspace{10 mm} j=1,....,n$

Now i have to show by test that we can assume the variance of Melbourne and Houston are the same.

I have understood how to test it.

$SSD_{1} = USS_{1}- \frac{S_{1}^{2}}{n_1} = 7864,32$
$s_{1}^2 = \frac{SSD_1}{f_{(1)}} = 655,36$

$SSD_{2} = USS_{2}- \frac{S_{2}^{2}}{n_2} = 12013,35$
$s_{2}^2 = \frac{SSD_2}{f_{(2)}} = 800,89$

$s^2_{numerator} = max\{s^2_{(1)},s^2_{2}\} and f_{numerator} is equal to the degree of freedom of s^2_{numerator}$

and

$s^2_{denominator} = min\{s^2_{(1)},s^2_{2}\} and f_{denominator} is equal to the degree of freedom of s^2_{denominator}$

$F=\frac{s^2_{numerator}}{s^2_{denominator}}=\frac{ 800,89}{655,36}=1,222$

$P_{obs}=2[1-F_{F_{(f_{numerator},f_{denominator})}}(F)]$

Thats how far ive gotten till now, and its pretty easy. What stops me is that i dont know how to find the $F_{F_{(f_{numerator},f_{denominator})}}(F)$ part.
I have a book of tables, where i can find $F_{p}(f_1, f_2)$, but apparently i dont know how to use it.
Could someone explain to me how to find it, or point me in the direction of a "guide"?..
If not, then id like the answer to $F_{F_{(f_{numerator},f_{denominator})}}(F)$, then i can just ask someone at the university to explain to me how it works.