I am testing pseudo-random number generators and need to perform a chi-squared test. However, I've encountered some difficulties.
Let's take the following example: I have generated 100 numbers, ranging from 1 to 10. The distribution is as follows:
1: 8
2: 12
3: 9
4: 11
5: 16
6: 6
7: 8
8: 10
9: 13
10: 7
From what I was able to understand, next I should calculate D.
$$D = d1 + d2 + d3 + ... + d10.$$
$di =$ square of the difference between the expected value and the observer value, everything over the expected value
$$d1 = ((8 - 10)^2)/10 = 4/10$$
$$d2 = ((12 - 10)^2)/10 = 4/10$$
. . .
$$d10 = ((7 - 10)^2)/10 = 9/10$$
Adding them up results in 84/10 or 8.4.
The next step is comparing this to $X^2$.
That is $X^2[1-\alpha,k-1]$. It is clear that $k=10$. But what value should I use for $\alpha$? And how to I know the value of $X^2$ after I decide what $\alpha$ I am going to use?
It feels that I am close but I just can't figure it out. Many thanks.