The Stinker Station convenience store chain wants to know if there is a differen

Question

The Stinker Station convenience store chain wants to know if there is a difference in miles per gallon a car would get using three different grades of gasoline: regular, mid-range and premium. Because of the differences in the performance of different automobiles, seven different automobiles were selected and treated as blocks. Therefore, each grade of gasoline was tested with each type of automobile. The results of the trials, in miles per gallon, are shown in the following table. At the 0.01 significance level, is there a difference in the types of gasoline or the different automobiles? List all the steps of the hypothesis test and do the calculations. Automobile Regular Mid-grade Premium

Automobile

Regular

Mid-grade

Premium

1

21

23

26

2

23

22

25

3

24

25

27

4

24

24

26

5

26

26

30

6

26

24

27

7

28

27

32

Automobile

Regular

Mid-grade

Premium

1

21

23

26

2

23

22

25

3

24

25

27

4

24

24

26

5

26

26

30

6

26

24

27

7

28

27

32

Explanation / Answer

Ho(automobile): there is no significant difference in the performance of different automobiles .

H1(automobile): there is a significant difference in the performance of different automobiles .

Ho(gasoline): there is no significant difference in the performance of different gasolines.

H1(gasoline): there is a significant difference in the performance of different gasolines.

Total sum of squares=13812-(287296/21)=13812-13680.7619=131.2381. Block sum of squares=[(4900/3)+(4900/3)+(5776/3)+(5476/3)+(6724/3)+(5929/3)+(7569/3)]-13680.7619=13758-13680.7619=77.2381.

Treatment sum of squares =[(29584/7)+(29241/7)+(37247/7)]-13680.7619=13724.5714-13680.7619=43.8095.

Error sum of squares=Total sum of squares-[Block sum of squares+Treatment sum of squares ]=131.2381-[77.2381+43.8095]=10.1905.

The table value of F at (2,12) , (6,12) is 6.927 & 4.821. Here Fcal > F tab, so we accept H1.

Therefore, H1(automobile): there is a significant difference in the performance of different automobiles & H1(gasoline): there is a significant difference in the performance of different gasolines.

Regular mid grade premium total squares 1 21 23 26 70 4900 2 23 22 25 70 4900 3 24 25 27 76 5776 4 24 24 26 74 5476 5 26 26 30 82 6724 6 26 24 27 77 5929 7 28 27 32 87 7569 Total 172 171 193 536 Squares 29584 29241 37247 287296

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