00:01
Okay, in this question, we're looking at the effectiveness of this leukemia serum, and we're trying to see if it works or not.
00:07
So really what we're trying to see is if the mean survival rate is, or survival time is the same for rats who have the treatment and who didn't.
00:18
If that's the case, then that means it's really not effective because it didn't change anything, or if we can reject that and say they're not the same, in which case it did something.
00:29
So, typically i know we're used to doing z scores and stuff here, but since the sample is only size 9 and it's less than 30, we have to do t.
00:38
So the first thing you can see that i have right here, i'm about to circle in red, this is the t score or the critical value.
00:47
This is how you calculate it.
00:50
So we need to find the mean, and we need to find the variance first.
00:54
So that's the first thing that we're going to do.
00:56
So let's look at all of our treatments for, well, let's look at the rats who had treatments in their survival time.
01:04
So that's 2 .1 plus 5 .5 plus 1 .2 plus 4 .4 plus 0 .7.
01:12
And then we divide that by there was a total of five rats.
01:16
And we get 2 .78.
01:18
Then let's come up with our second mean which comes from the non -treatment that's 1 .9 plus 0 .6 plus 2 .6 plus 3 .3 divide that by 4 and that is 2 .1 now it's time to come up with the variance as you can see that's in our formula and i wrote the formula of refining the variance here you're going to just take each of the values subtract the mean and square them add them all up and then we will divide by n minus 1.
01:55
So i have 2 .1 minus 2 .78 squared, plus 5 .5 minus 2 .78 squared, plus 1 .2 minus 2 .78 squared, plus 4 .4 minus 2 .78 squared.
02:13
Plus 0 .7 minus 2 .78 squared.
02:19
Let's go ahead and find what that actually gives us.
02:25
You're going to need a calculator for this 2 .1 minus 2 .78 squared is 0 .4624 plus 5 .5 minus 2 .78 is 2 .72.
02:45
Squared is 7 .3984 plus i'll do 1 .2 minus 2 .782 squared is 2 .782.
02:47
Squared is 39984 plus.
02:50
I'll do 1 .2 minus 2 .78 2 .4964 plus 4 .4 minus 2 .78 squared is 7 .7284.
03:17
And then we do plus and 0 .7 minus 2 .78 squared.
03:24
Is 0 .8464.
03:32
So now we're going to add it all together because we have to sum it up and divide by n minus 1.
03:37
So we're going to add all these values up together .4624 plus 7 .3 -984 plus 2 .9664 .2 .9664 plus 7 .7284 plus is 18 .932.
04:13
We're going to divide that by n minus 1.
04:15
Since there are five rats that we're testing here in our sample, we subtract one from that.
04:19
So it's four.
04:20
So we're going to divide by four.
04:23
And that gives us 4 .733.
04:27
Okay, so that's our first variance.
04:29
Over here, i calculated the second variance.
04:33
It works the same way where you just take each value, subtract 2 .1 and square it.
04:38
So 1 .9 minus 2 .1.
04:41
Squared is 0 .04.
04:44
0 .6 minus 2 .1 squared is 2 .25.
04:52
2 .6 minus 2 .1 squared is 0 .25.
04:59
And then 3 .3 minus 2 .14 .4.
05:06
We added all of those up again.
05:07
So 0 .05 plus 2 .25 plus 0 .4 .4 plus 0 .4 .5.
05:10
Plus 0 .4 .4 .5.
05:12
Point 25 plus 1 .44, we get 3 .98, and then we divide that by n minus 1.
05:18
And there were only four rats that were not treated.
05:21
So 4 minus 1 is 3...