00:01
Alright, in your question you're given data about the age and the favorite type of reading for 779 randomly selected people.
00:08
We're to test the claim that age and preferred reading type are independent.
00:15
It says use alpha level .05.
00:19
What this is, this will be a chi -squared test of independence.
00:28
And the first thing that was required of me is to go ahead and make totals for all the columns and all the rows.
00:38
And then i have another table set up for where we're going to put the expected counts.
00:49
Alright, to calculate the expected counts we take the row total, so i'm going to work on the expected count for this value right here.
00:57
I take the row total, i'm sorry, let's just do the column total, 214, times the row total, 189, and we divide that by the total overall, 779.
01:15
And that works out to be 51 .92 approximately.
01:22
I'm going to try to round everything to two decimal places for my, uh, what work i put on the screen, but i have all these decimal values on my calculator throughout the problem.
01:33
We'll go 51 .92.
01:36
Let's do one more of those.
01:38
So let's do the mystery one right here.
01:42
The column total is 186, times the row total for 45 is the 189 that we just used, divided by 779.
02:02
That works out to be 42 .13.
02:09
Alright, so i'm going to pause the video and find the rest of the expected counts the exact same way, taking row total times column total divided by overall total.
02:32
I'll be right back.
02:36
Alright, so as you can see i've completed the expected counts table.
02:40
Again, taking row total times column total divided by overall total.
02:46
Now we're going to go ahead and calculate our chi -squared test statistic.
02:51
It equals the sum of the observed value minus the expected value squared divided by the expected.
03:05
Okay, so what that's going to look like, i'll start and i'll work my way across the first row here.
03:11
It'll be 21 minus the expected was 51 .92 squared divided by 51 .92.
03:23
Plus, and now i have to do that for the next value, 45 minus the expected, 42 .13 for that column...