00:01
All right, so i'll be doing this problem in excel, though i'll be doing most of the analysis, basically by hand, or at least step by step.
00:09
I'm just using excel as a fancy calculator effectively.
00:12
So first thing that i'm doing here, just to get part or get the first part of the problem out of the way, is creating a scatter plot so we can compare those to the, or compare to the different options.
00:24
So looking at it, we can see that this would most closely resemble option d.
00:29
So for the first, for the first part of the problem, the correct graph is graph d.
00:34
Now, for finding the correlation coefficient, i'll note this off to the side here, the correlation coefficient is the sum of squared deviations for products divided by the square root of the sum of squared deviations for x times the sum of squared deviations for y.
00:55
So to find those, the first step that we need to take is to find the average x and y values.
01:01
Pretty straightforward calculation.
01:03
Of course, we just add up all of the values and divide by the number of values.
01:08
Or in my case here, i am using excel just to sort of speed along through that.
01:13
So we have our x bar and y bar values here.
01:16
Now, in order to find the different ss values, ssx, x, ss, x, y.
01:23
No, i want capital s's.
01:25
There we go.
01:26
And ssyy, what i'll do is set up a column of x minus x bar squared, x minus x bar times y minus y bar, and y minus y bar squared.
01:45
So ssx is going to be the sum of everything in the x minus x bar squared column.
01:53
Ssxy is going to be the sum of everything in the x minus x bar squared column.
01:57
Y minus y bar column and s s yy is going to be the sum of everything in the y minus y bar squared column so i'll now just fill out those columns so for instance for the first x value it would be 29 minus x bar so that's 38 .92 roughly i'm putting in an explicit reference reference to b15 we'd get oh wait still need to square that that.
02:30
So 29 minus 38 .92 roughly gives us 98 .34.
02:34
Then we want to apply that same procedure for each one of the following values.
02:40
Then similarly for the x minus x bar times y minus y bar column, well, we would do 29 minus b15, so minus 38 .92 roughly times 45 from cell b2 minus the y bar value from cell b 16 we get 19 .833 for that first element or that first pair and then lastly we just need to do the y minus y bar squared so that would be 45 from cell b2 minus 47 from cell b 16 are up 2 so we get a result of 4 apply that down so now we have our s s x s xy and ss y yy so using the formula off to the side there, the correlation coefficient r, it's going to be equal to ssxy, divided by the square root of ssxx times ssy.
03:44
So we get that our correlation coefficient is negative 0 .2067, and that should be lowercase r.
03:54
Now, we have that the null hypothesis would be that the population correlation is equal to zero, and the all the alternate hypothesis is, yeah, so the claim is that there is a correlation, so the alternate hypothesis is that the correlation does not equal zero.
04:16
The test statistic, t, we calculate using the formula, t equals r, oh, oops, t equals r times the square root of n minus 2 divided by 1 minus r squared...