00:01
All right, so we have a problem about the gpas.
00:02
We have four students with gpa is 2, 3, 3, and 4.
00:06
Age of the students are 10, 11, 12, and 15 respectively here.
00:10
In total, there are 10 ,000 total students.
00:19
So we have the average gpa is unknown, but the standard deviation of the gpa is 0 .02.
00:26
And it's normal.
00:27
That's good to know.
00:28
So we can use our z score to get our confidence interval.
00:37
So let's do the mean standard deviation first.
00:40
So the mean for the gpa is three standard deviation.
00:48
The sample standard deviation that is is 0 .816.
00:52
I use the spreadsheet to do it for me.
00:54
Just remember to do the sample standard deviation, which is s.
01:00
That's how my my spreadsheet does it.
01:02
P for population, but that's a simple.
01:05
Now to do the confidence interval.
01:08
So the z star, that means you have to account for the alpha.
01:11
So it's like z alpha over two.
01:17
So what that means is we want 90, so it's around like 0 .05 over 2.
01:22
So we're looking for a z .025.
01:26
That's going to be the z score.
01:29
So the little normal lookup.
01:31
I have a norm s in.
01:32
That's the function that does it.
01:34
I want 0 .025.
01:37
That's the score i'm looking conformable, but it's actually the, that's the corresponding z score, but that's the plus or minus because that kind of keeps us within that range.
01:49
So that's the z we're going to use, and let's go into this.
01:53
So we have a lower, upper bound here, lower is equal to the mean, which is three minus z score of 1 .96 times the population, standard deviation.
02:14
Which is 0 .02.
02:18
We'll divide that by the square of four.
02:23
They're lower, or upper.
02:26
It would be the exact same except plus.
02:31
That's our confidence interval.
02:37
Because the n refers to how many in the mean here.
02:43
10 ,000 is kind of a distraction.
02:48
So there's our interval.
02:49
You might see it written as so our 95 % ci is given as, it may see it like this.
03:01
2 .892 to 3 .02, like that.
03:08
It's in that interval notation.
03:12
All right, so now we're going to use the correlation formula to find r.
03:16
It's this thing, so we just do a little bit of work.
03:19
Let me just to the side.
03:24
So we need to find the difference in the x.
03:27
So it's called the products, which is x minus x bar times y minus y bar.
03:37
So we'll do it all together...