00:01
Ok, so what we're going to use in this question is that the total sum of squares is equal to the sum of squares between plus the sum of squares within and the same for the degrees of freedom.
00:13
We're also going to use the fact that the mean square is given by the sum of squares divided by the degrees of freedom for that row and that the f test statistic is given by the mean square for between the groups divided by the mean square for within the groups.
00:29
So these are going to be what we're going to use to answer this question.
00:32
So for part a, we need the degrees of freedom for between the groups to start off with.
00:41
We've been given some data points.
00:52
So we can see using this formula that the degrees of freedom is just going to be the sum of squares divided by the mean square, which here turns out to be three.
01:01
That gives us a total of 23 degrees of freedom.
01:04
The mean square for within the groups using this is going to be the mean square for between the groups divided by the f -test statistic, which is 0 .944.
01:16
And the sum of square for within the groups then using this is going to be 20 times 0 .944, which gives us 18 .88 and a total of 21 .004.
01:30
For table b, we can first work out the mean square for between the groups, which is, well, in fact, we're going to do it this way instead, just because i found that the decimal places work slightly nicer.
01:57
So we'll work out the sum of squares for within the groups, which is just going to be these two things times together using our formula at the top.
02:06
And that gives us 168 .66...