00:01
For this question, we have a dealer who has stocked in, who has stocked three cars, model a, b, and c, and of the same make, but different models.
00:10
So we're going to come, it gives us a table to compare the mileage obtained for the three models and a customer to test each car with three brands of gasoline, x, y, z.
00:22
And in each trial, a gallon of gasoline was added to an empty tank and the car was driven without stopping until we were.
00:30
Ran out of gasoline.
00:31
Now we have a table that shows the number of mouse covered in each of the nine trials and we're answering questions.
00:38
So i'll be drawing the graph, the table so we can understand better and the distance is a mile.
00:45
So the brand of gasoline, according to the question, is x, y and z.
00:56
There we have a model a, model a, model b, and model c, and their distance is a so for model a, brand of gasoline is 22 .4, 4, 4, 20 .8, 21 .5, and this 17 .0, 19 .4, 18 .7, 19 .2, 20 .2, and 21 .2.
01:28
Now, the first question wants us to know, should the customer conclude that different car models differ in mean gas mileage and test at a equals to point five level so we're giving that n the total of experimental units is equal to nine right and we're giving that k the number of treatment of the car models is equal to three because the three models and be the number of blocks the brand the brand of gas is equal to 3 so if you're given all these 3 without our values of the quantity necessary to compute the value of f statistics would be c m is equal to submission 3 i is equal to 1 summation 3 j is equal to 1 y i j close bracket squared divided by n divided by n divided by n and this will give you 180 .4 squared divided by 9 and this will give you 3616 .017.
03:04
Now the total ss is equal to summation 3 i is equal to one.
03:15
Summission 3 the j is equal to 1 over here the yij 3 minus c m now, if you calculate this, you get 3637 .82 minus 3616 .017.
03:34
And this gives you 21 .803.
03:49
Now, sst is equal to submission 3.
03:54
I is equal to 1 y squared i divided by b minus t .m.
04:04
And this is equal to 3631 .486 minus 3616 .017.
04:15
It is equal to 15 .469.
04:21
Ssb is equal to summation 3j is equal to 1.
04:29
Yj squared divided by k, cm minus cm.
04:35
This is equal to 3617.
04:38
Point 35 minus 3616 .017 and this will give you 1 .343 right now sse is equal to c s s s t minus s b this is equal to 21 .803 minus 603 minus 15 .469 minus 1 .3 this is equal to 4 .991 now the observed values of ms t and ms e are ms t is equal to sst divided by k minus 1 this will give you 15 .469 divided by 2 and this will give you 7 .774 now ms e is equal to sse divided by n minus k minus e plus 1.
05:49
And this will give you 4 .991 divided by 4.
05:53
And this will give you 12 .1 .247.
05:59
Right.
06:00
So now the observed value of f statistic to test the no hypothesis, which is the different car modules, same in mean gas mileage...