00:01
All right, so we have a nice little exercise involving the kai squared distribution.
00:07
So each day's proportion of one week's total truck traffic is shown here.
00:14
And during the same week, the number of overweight trucks per day is given in the second column right here.
00:20
Determine whether the number of overweight trucks per week is distributed over the seven days of the week in direct proportion to the volume of truck traffic using alpha 0 .1.
00:32
0 .1.
00:34
So what that means is we're looking for is the proportion of traffic equal to the amount of overweight traffic that we see proportional to the total traffic going through.
00:52
So the way i did this, well here's the proportions and then here's the observed counts that we saw.
01:02
So we want to see is this proportion is the observed overweight trucks in direct proportion? are they the same as the proportion of traffic throughout the week? and so looking at the first part of it, determine the null and alternative hypotheses.
01:24
So it's c.
01:30
We're not asking, are these p's all the same? because this is like our model.
01:40
This is our model that we're using.
01:43
The proportion, this is what we observe.
01:46
We're given that that is the case for all the proportions of the overweight cars.
01:52
And the alternative is at least one of these probabilities does not equal its hypothesized value.
01:59
So this would be like p1, p2.
02:03
Well, let me do it here.
02:05
Here's your p1 value here.
02:08
Well, ends up being, this is your p1 value.
02:25
There we go.
02:26
P1 value, p2 value, p3 value, p4, six.
02:42
And then what you do, the way you calculate this, is this is our observed values are here, and what we'd expect is given here.
02:51
And the way you calculate your expected value is your take your proportion here times, well, how many we saw.
02:59
We saw a total of 440 overweight cars over the week.
03:10
And the question is, are those 448, or excuse me, overweight trucks, that is, are those overweight trucks distributed in the same proportion as we see total truck traffic? and so the way we do this is we say, okay, this proportion here would give us an expected value of 84 .92 because you take your p, your proportion times 440 is what we would expect.
03:43
And we're seeing how far off is expected from the observed.
03:47
And what you do to figure this out is you do this calculation, the observe minus expected squared over expected.
03:54
And then the kye squared value is equal to the sum of your observed minus your expected values over expected.
04:05
And you take the sum is like that encapsulates encapsulates the whole fraction here.
04:15
It's like that...