00:01
So we can have some data from an experiment that was performed to investigate the best way to produce a chemical solution.
00:07
So there's three different methods, a, b, and c.
00:12
And the various trials are conducted with each method.
00:16
And we're looking at the resulting solutions are classified as being weak, satisfactory, or strong.
00:22
Or too strong, i should say.
00:23
So weak, too strong, and satisfactory.
00:26
This is what we're looking for.
00:27
This is too strong.
00:28
And we're going to test at the alpha of 0 .05 level of significance if there's some some correlation between the method and the solution classification.
00:41
So the first thing we're asked is what's the sample size and to do that you sum up all of the values in the table.
00:47
So i've gone ahead and done that and i've actually i've done more i've summed across the row each method a, b, and c.
00:52
So 71 for a, 126 for b and 7 for c.
00:56
And you add those up you get 268.
00:58
I've also added up the columns for weak, satisfactory, and strong as well.
01:01
These are called your marginal counts because it's on the margin of your data table.
01:06
So for a the answer m is 268.
01:21
Question b asks us what's the expected count for the observed count of 11? so we observe this.
01:28
This is the observed method a, weak.
01:33
Weak number frequency.
01:35
We observed as 11.
01:37
What's the expected? well, you find the expected value by taking the total in the row, multiplied by the total in the column, divided by the total in the table, which i guess would be n.
01:50
So total in the row, 71.
01:53
Total in the column is 50.
01:58
And then divided by 268.
02:00
And that number is 13 .2462.
02:08
And let me clean this up a little bit for us.
02:18
So i've done it for all of the values actually.
02:21
So, but the way, you know, so this 13 .24 came from the total in the row, times the total in the column, divided by the synthesized.
02:30
And if you do that for all nine cells, like this one, 23 .5 came from 126, times 50 divided by 268...