00:01
We have been provided the data that shows the age and favorite type of music of 79 randomly selected people.
00:08
And the test, we have been asked the test of saying that the age and preferred music type are independent.
00:13
And here, alpha is given to be 0 .05, that is the level of significance.
00:21
Now here, we have to first formulate the null hypothesis and the alternate hypothesis for this.
00:27
So the null hypothesis would be that the two categorical variables, that is the music type and age are independent.
00:45
And the alternative hypothesis would be that music type and age are dependent, with the level of significance of 0 .0 .0.
00:59
Now first of all we have to calculate the test statistics for the expected values okay right so here we will add one more column that is we have to total the all all of the values here so the total of these four types of music is will be 189 and the four of this will be 213 then there will be to 000 and the total of this will be 177 8 and we add one row here that tells the total of the roll and total of the column so here it will be 214 186 and 188 and 191 and the total here it should be 779 because the total of the total of the people that have been selected are 779 right so so here we need all right the expected values that is e is equal to the total of the rows multiplied by the total of the columns and divided by the total number of the data which we have been used so it will be 189 into 240 and multiplied by 770 that will be 51 .92 so that's how we calculate the expected values right so let's just formulate the table that is first column would be the observed value then we calculate the expected value of each then the difference between the two then the square of this so this is basically the how we are performing here test at least for the five square analysis and the kai square will be here square divided by the expected value that is e right so so first we have is 21 of both value and for that the expected value is 51 .92 and o minus e will be minus 30 .92 6 .0 7 then it will be 80 .41 right next is 45 so it will be 45 .13 minus 0 .13 0 .02 and it will be 0 .0.
03:59
Next your value is 90 that comes to be 45 .61, 44 .39, 1970 .27 and 43 .20.
04:14
In the next it will come 33 that is 46 .3.
04:19
14 .34 .94 .963 .1884 and we have to calculate this for all the values that have been observed right 9 .49 .1 .54 then comes 55 to 0 .864 .14.
04:53
Then 0 .85 .04.
04:53
10 .850 .5 .0 .3 .34.
05:07
48 65 then 47 let's calculate to here first for 42 it will be 51 .409 .40 8 .44 1 .7 to 22 to 22 17 .85 and 0 .365 and 0 .65 for for 65 it will be 54 .9 .04 10 .0 .0 .0 .6 65 it will be 54 .94 10 .0.
05:48
1 .16 and 1 .8 and 4 for this it will be 47 .75 minus 0 .75 0 .57101.
06:05
After that comes the next value is 31 57 60 39 25 and 53 so these are the values that we need to calculate for 0 .27 minus 17 .27.
06:34
0 .97.
06:34
28 .15 and 6 .18.
06:37
8 will be 49 .04...