00:01
So in this question we have a claim.
00:04
And the claim is that when we look at age and the proportion of gun deaths that happen at that age, we have 0 to 19 and the probability is 0 .1, 20 to 44, the probability is 0 .5, and 45 plus the probability is 0 .4.
00:32
But now we have a random sample of deaths by firearms.
00:40
So now we have age and the frequency.
00:48
And so for 0 to 19, we have 13 victims.
00:57
For 20 to 44, we had 62 victims.
01:01
And for 45 plus, we have the remaining.
01:07
So out of 100.
01:07
So that's 100 minus 62 minus 13 because there's a total of 100 and that's 25.
01:16
So now what about the expected frequency if the claim is to be believed? so claim frequency.
01:25
Well, since there are 100 people in the sample, this is easy because we can just multiply 100 by these quantities here.
01:34
So we get 10, 50 and 40.
01:39
So now we've got our frequencies and our claim frequencies.
01:43
We can do a kye squared test.
01:45
So the null hypothesis for this kai squared test is that the claim is true, and the alternate hypothesis is going to be that the data shows significant deviation from the claim.
02:15
So we can work out kye squared now.
02:17
Kye squared is going to be the sum over our ages of the difference in frequencies squared.
02:24
So sum over ages, frequency minus expected frequency squared over the expected frequency.
02:38
So what does this give us? so we get 3 squared over 10 plus 12 squared over 50 plus 15 squared over 40.
02:49
To give us a kye squared of 9 .405...
