Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

Engineers are testing company fleet vehicle fuel economy (miles per gallon) perf

ID: 3207675 • Letter: E

Question

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?

                87 Octane           89 Octane           91 Octane           Ethanol 5%          Ethanol 10%

Compact            30.4                      29.4                      18.9                      30.1                      27.8       

Mid-Size            17.0                      19.3                      17.8                      17.0                      31.9       

Full-Size             27.7                      28.3                      21.4                      29.7                      31.1       

SUV                 23.5                        21.4                      18.4                      19.6                      28.7       

                Choose the correct statement.

                1. Fuel type is the blocking factor and vehicle size is the treatment.

                2. Fuel type is the treatment and vehicle size is the blocking factor.

Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

    

                                                                    Two-Factor ANOVA

Source SS                                                   df               MS         F              p-value

Treatments (Vehicle Size)                          ?             ?              ?                 ?

Blocks (Fuel Type)                                      ?             ?                ?                  ?

Error                                                                ?         ?                  ?                    -  

Total                                                                  ?         ?                 -                  -

Group                                                  Mean             n        Std. Dev

    87 Octane

    89 Octane

    91 Octane

   Ethanol 5%

    Ethanol 10%                                 

    Compact         

    Mid-Size         

   Full-Size          

       SUV

    Total:

Choose the correct statement. Use = 0.05.

                Fuel type means differ significantly, but vehicle size is not a significant factor.

                Fuel type means differ significantly and vehicle size is also a significant factor.

                Fuel type means do not differ significantly and vehicle size is not a significant factor.

                Fuel type means do not differ significantly, but vehicle size is a significant factor.

Which fuel types show a significant difference in average fuel economy? Use the Tukey simultaneous comparisons at = 0.01.

                Ethanol 10% and Ethanol 5%

                87 Octane and 89 Octane

                Ethanol 5% and 91 Octane

                Ethanol 10% and 91 Octane

Explanation / Answer

Result:

Choose the correct statement.

                1. Fuel type is the blocking factor and vehicle size is the treatment.

                2. Fuel type is the treatment and vehicle size is the blocking factor.

Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

Randomized blocks ANOVA

Mean

n

Std. Dev

24.6500

4

5.8370

87Octane   

24.6000

4

5.0020

89Octane   

19.1250

4

1.5819

91Octane   

24.1000

4

6.7828

Ethanol5%  

29.8750

4

1.9397

Ethanol10%

27.3200

5

4.8132

Compact    

20.6000

5

6.3863

Mid-Size    

27.6400

5

3.7280

Full-Size     

22.3200

5

4.0530

SUV    

24.4700

20

5.4578

Total

ANOVA table

Source

SS

   df

MS

F

   p-value

Treatments

231.877

4

57.969

4.79

.0153

Blocks

188.854

3

62.951

5.20

.0157

Error

145.231

12

12.103

Total

565.962

19

Choose the correct statement. Use = 0.05.

                Fuel type means differ significantly, but vehicle size is not a significant factor.

               Answer: Fuel type means differ significantly and vehicle size is also a significant factor.

                Fuel type means do not differ significantly and vehicle size is not a significant factor.

                Fuel type means do not differ significantly, but vehicle size is a significant factor.

Which fuel types show a significant difference in average fuel economy? Use the Tukey simultaneous comparisons at = 0.01.

                Ethanol 10% and Ethanol 5%

                87 Octane and 89 Octane

                Ethanol 5% and 91 Octane

                Answer: Ethanol 10% and 91 Octane

Tukey simultaneous comparison t-values (d.f. = 12)

91Octane   

Ethanol5%  

89Octane   

87Octane   

Ethanol10%

19.1250

24.1000

24.6000

24.6500

29.8750

91Octane   

19.1250

Ethanol5%  

24.1000

2.02

89Octane   

24.6000

2.23

0.20

87Octane   

24.6500

2.25

0.22

0.02

Ethanol10%

29.8750

4.37

2.35

2.14

2.12

               critical values for experimentwise error rate:

0.05

3.19

0.01

4.13

Randomized blocks ANOVA

Mean

n

Std. Dev

24.6500

4

5.8370

87Octane   

24.6000

4

5.0020

89Octane   

19.1250

4

1.5819

91Octane   

24.1000

4

6.7828

Ethanol5%  

29.8750

4

1.9397

Ethanol10%

27.3200

5

4.8132

Compact    

20.6000

5

6.3863

Mid-Size    

27.6400

5

3.7280

Full-Size     

22.3200

5

4.0530

SUV    

24.4700

20

5.4578

Total

ANOVA table

Source

SS

   df

MS

F

   p-value

Treatments

231.877

4

57.969

4.79

.0153

Blocks

188.854

3

62.951

5.20

.0157

Error

145.231

12

12.103

Total

565.962

19