Question

As part of a study designed to compare hybrid and similarly equipped conventional vehicles, Consumer Reports tested a variety of classes of hybrid and all-gas model cars and sport utility vehicles (SUVs). The following data show the miles-per-gallon rating Consumer Reports obtained for two hybrid small cars, two hybrid midsize cars, two hybrid small SUVs, and two hybrid midsize SUVs; also shown are the miles per gallon obtained for eight similarly equipped conventional models. Dataset: CarModels

1. What are the treatment(s) and how many are there?
2. What is the number of observations in each treatment and the total number of observations?
3. Create a table with the marginal means of this factorial design. Draw an interaction plot.
4. Are there any interactions between the factors? Why?
5. Set up an ANOVA Table. Do the proper tests.
6. Is it necessary to continue? Explain. Even if not, still answer next question.
7. Test for differences in means for Factor A and Factor B.

   Make/Model	Class	Type	MPG
   Honda Civic	Small Car	Hybrid	37
   Honda Civic	Small Car	Conventional	28
   Toyota Prius	Small Car	Hybrid	44
   Toyota Corolla	Small Car	Conventional	32
   Chevrolet Malibu	Midsize Car	Hybrid	27
   Chevrolet Malibu	Midsize Car	Conventional	23
   Nissan Altima	Midsize Car	Hybrid	32
   Nissan Altima	Midsize Car	Conventional	25
   Ford Escape	Small SUV	Hybrid	27
   Ford Escape	Small SUV	Conventional	21
   Saturn Vue	Small SUV	Hybrid	28
   Saturn Vue	Small SUV	Conventional	22
   Lexus RX	Midsize SUV	Hybrid	23
   Lexus RX	Midsize SUV	Conventional	19
   Toyota Highlander	Midsize SUV	Hybrid	24
   Toyota Highlander	Midsize SUV	Conventional	18

Answer 1

small car midsize ca small SUV midsize SU Hybrid conventional 44 28 32 32 23 25 28 21 22 19 18

there are total 2*2*4 = 16 observation
there are 2 factors
4 levels for class and 2 levels for Type

small car midsize ca small SUV midsize SU Total SUMMARY Hybrid Count Sum Average Variance - 2 81 40.5 24.5 2 59 29.5 12.5 2 55 27.5 0.5 28 47 242 23.5 30.25 0.5 50.78571 conventional Count Sum Average Variance 2 60 2 4 8 24 2 2 43 21.5 0.5 2 37 18.5 0.5 8 188 23.5 22 30 8 Count Sum Average Variance Total 1 4 4 4 4 141 107 98 84 35.25 26.75 24.5 21 47.58333 14.91667 12.33333 8.666667 35.25 107

Using Excel

data -> data analysis -> Anova: Two-Factor With ReplicationANOVA

df F ANOVA Source of Variation Sample Columns Interaction Within SS 182.25 441.25 19.25 MS 1 182.2500 3 147.0833 3 6.4167 8 6.1250 29.7551 24.0136 1.0476 P-value 0.0006 0.0002 0.4229 Ecrit 5.3177 4.0662 4.0662 49 Total 691.75 15

The p-value for Factor A is less than .01

Factor A is significant

The p-value for Factor B is less than .01,

Factor B is significant

The p-value for the interaction of factors A and B is greater than .10

The interaction of factors A and B is not significant