00:01
We have these five numbers that were generated, and it's desired to perform a test for uniformity by using a chi -squared test.
00:09
And we use the alpha of 0 .05 level of significance.
00:13
And so we're doing a chi -squared test for uniformity, basically testing if these could have come from a uniform distribution.
00:23
And we're gonna use a chi -squared test.
00:24
Before we started about the formula, the way we think about this as a uniform, well, these are the values.
00:29
Let's sort them out.
00:30
We're gonna see what they would look like.
00:33
So they started out here.
00:34
This is gonna help us here.
00:35
Because if they're uniform, that means it's evenly distributed amongst zero to one.
00:41
We're gonna go and assume a uniform of zero to one.
00:44
And so zero to one, now we've got five values.
00:48
If they were to be the case, we would have come from uniform distribution.
00:53
We have essentially an equal amount in zero to 0 .2, zero to 0 .4, zero to 0 .6, and zero to 0 .8, and zero to 0 .8 to one.
01:05
Sorry, i think i said that wrong.
01:06
Zero to 0 .2, 0 .2 to 0 .4, 0 .4 to 0 .6, and 0 .6 to 0 .8, and 0 .8 to 0 .1.
01:11
There, that's what i meant to say.
01:12
So you'd have an evenly distributed, even amount in these categories.
01:17
Because we use a chi -squared test for counts in categories.
01:20
So our categories are zero to 0 .2, 0 .2 to 0 .4, 0 .4 to 0 .6, 0 .6 to 0 .8, 0 .8.
01:34
And we look at how many of these values, and i sorted them here, how many of these values fall in these categories? well, there are two in the zero to 0 .2, right? there's these two values, 0 .05 and 0 .14.
01:49
That fall to those two there and here.
01:51
There are none of the 0 .2 to 0 .4 category.
01:53
There's one in the 0 .4 to 0 .6, there's that one.
01:56
There's zero in the 0 .6 to 0 .8, but there's two in the 0 .8 to 0 .1, there'd be two values.
02:02
Count them up.
02:02
Well, if they were evenly distributed, uniformly distributed random variables, we would expect one in each category.
02:11
We'd expect one.
02:12
Now we're getting to our chi -squared statistic...