00:01
We are given in the question with following table and we have to construct the expected values for the table and find if these variables are independent at 1 % significance level.
00:17
So for this, let us firstly complete this table.
00:21
For that, let us find the total number of persons, whether smokers or non -smokers suffering from emphyseemia, they will be 20 plus 60.
00:31
That is 80 and 70 plus 180 that is 150 and it is 70.
00:41
Similarly finding totals of smokers and non -smokers it will be for known smokers 120 and for smokers it is 180.
00:54
So now let us find the expected values.
00:58
Expected values for emphyseemia will be 120 as there are emphysemia and non -smokers.
01:08
So it is 120, multiply 80.
01:12
Out of how many, it is 300.
01:17
As total are 300 from both this side and this side.
01:24
So for non -smokers and emphysemia, it is 120, multiply 80, divide 300.
01:36
120, multiply 80 divide 300, which will be 32.
01:47
Similarly, calculating for smokers, it will be 180, multiply 80, divide 300, which will be 180, multiply 80, divide 300 is 48.
02:08
Similarly, calculating for a heart problem, it will be 60, 90 and for cancer it comes out to be 28 and 42.
02:24
Now let us find test statistics.
02:34
We know that formula for test statistics that is sky square is equal to summation oi that is observed value minus expected value...