00:01
So we have some data here, item one through nine, these three different supermarkets.
00:05
And each of these three supermarket chains in this denver area claims to have the lowest overall prices.
00:12
And to study this, a local tv station randomly selected nine grocery items.
00:19
That's what these items are.
00:20
And on the same day, there was an intern that was sent to each of these three different stores and purchased the nine items.
00:27
And so this is, so these, like for example, item one at this one store was $1 .12, ralph's was $1 .02 and loblaw's was $1 .07.
00:36
And then that's how we read this data.
00:39
And so what we're looking at essentially is a one -way anova and our null hypothesis is that the means are all the same.
00:47
So the mean of group one, so we'll call the super dollar sign, we'll call it group one, ralph's group two, and then loblaw's group three.
00:54
So we'll say the mean of one is equal to the mean of two, is equal to the mean of three.
00:58
So all means are equal.
00:59
Against the alternative, all the means are not equal.
01:12
All right, so here we go.
01:14
So we're going to test this pair of hypotheses at the alpha of 0 .05 level of significance.
01:22
And we're gonna test this alpha against the p -value we get from our anova and we get the f -statistic.
01:32
And we're gonna reject h -naught if our p -value that we get is less than the alpha of 0 .05.
01:49
Okay.
01:50
Now let's go ahead and get our statistic, f -statistic, and where our p -value is gonna come last, we need the f -statistic.
01:58
So the f -statistic is found by taking the mean square of the between groups divided by the mean square of the within groups.
02:06
We don't have that yet.
02:07
So we got the mean squares.
02:08
The mean squares of the between groups, so this one, is equal to the sum of squares of the between groups divided by the degrees of freedom.
02:18
The mean square of the within groups is the sum of squares of the within divided by the degrees of freedom of the within.
02:26
And to write dfb for the between groups there.
02:29
Great.
02:30
We don't have those yet.
02:31
So now we need the sum of squares.
02:33
The sum of squares for the, there's a few ways you could do this.
02:38
The way i did this is i found the total first and then the between and then the within.
02:42
And let me show you why.
02:44
Because the sum of squares of the total is equal to the sum of squares of the between plus the sum of squares of the within.
02:50
So if we have the total in the between, we just take the difference and that gets us our within.
02:54
So let's go ahead and get our sum of squares of the total.
02:57
This is equal to the sum of each individual x value, all these 27 values, right? there's 27 of these values, minus the grand mean x bar sub g squared.
03:09
That's the sum of squares of the total.
03:13
So we're gonna find that grand mean, we'll be good to go.
03:15
And then the sum of squares of the between is equal to the sum of each group's mean on x bar, we'll say i, and then this is gonna iterate from i equals one to k, where k is number of groups, where k is three, minus the grand mean squared multiplied by n sub i, which is the number of, in each group.
03:42
And they're all nine.
03:43
All of this is actually gonna be nine.
03:44
So for our purposes, this is all nine.
03:46
All right, so let's go ahead and do that.
03:50
So here are the means of each group, right there.
04:01
Here's the grand mean, 3 .1001481481.
04:07
Please be aware, i didn't round it all...