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) were tested. 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.

Make/Model	Class	Type	MPG
Honda Civic	Small Car	Hybrid	36
Honda Civic	Small Car	Conventional	28
Toyota Prius	Small Car	Hybrid	44
Toyota Corolla	Small Car	Conventional	33
Chevrolet Malibu	Midsize Car	Hybrid	26
Chevrolet Malibu	Midsize Car	Conventional	22
Nissan Altima	Midsize Car	Hybrid	31
Nissan Altima	Midsize Car	Conventional	26
Ford Escape	Small SUV	Hybrid	27
Ford Escape	Small SUV	Conventional	20
Saturn Vue	Small SUV	Hybrid	28
Saturn Vue	Small SUV	Conventional	22
Lexus RX	Midsize SUV	Hybrid	24
Lexus RX	Midsize SUV	Conventional	19
Toyota Highlander	Midsize SUV	Hybrid	23
Toyota Highlander	Midsize SUV	Conventional	17

At the  level of significance, test for significant effects due to class, type, and interaction.

Assume that Factor A is Class of vehicle tested and Factor B is Type.

Source of Variation	Sum of Squares (to 2 decimals)	Degrees of Freedom	Mean Square (to 2 decimals)	F (to 2 decimals)
Factor A
Factor B
Interaction
Error
Total

The p-value for Factor A is - Select your answer from the following: less than .01, between .01 and .025, between .025 and .05, between .05 and .10, or greater than .10

What is your conclusion with respect to Factor A?

- Select your answer from the following - Factor A is not significant OR Factor A is significant

The pvalue for Factor B is - Select your answer from the following - less than .01, between .01 and .025, between .025 and .05, between .05 and .10, OR greater than .10

What is your conclusion with respect to Factor B?

- Select your answer from the following - Factor B is not significant OR Factor B is significant

The p-value for the interaction of factors A and B is - Select your answer - less than .01, between .01 and .025, between .025 and .05, between .05 and .10 OR greater than .10

What is your conclusion with respect to the interaction of Factors A and B?

- Select your answer - The interaction of factors A and B is not significant OR The interaction of factors A and B is significant

Answer 1

Assuming that Factor A is Class of vehicle tested and Factor B is Type, the 4x2 ANOVA table is obtained as follow

		Factor A
		Small Car	Midsize Car	Small SUV	Midsize SUV
Factor B	Hybrid	36	26	27	24
		44	31	28	23
	Conventional	28	22	20	19
		33	26	22	17

Now, the ANOVA model for the mlg is obtained in EXCEL by using following step;

Step 1: Write the data value in excel. The screenshot is shown below;

Step 2: Data>Data Analysis>Two-Factor With Replication>OK. The screenshot is shown below:

Step 3: Select>Input Range>OK., Rows per sample: 2, Alpha value = 0.05 at 5% significance level. The screenshot is shown below;

The result is obatained. The screenshot for ANOVA table is shown below,

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	458.75	3	152.92	17.48	0.00	4.07
Factor B	169	1	169.00	19.31	0.00	5.32
Interaction	14	3	4.67	0.53	0.67	4.07
Error	70	8	8.75
Total	711.75	15

Correct answer:

	p-value			significant?
Factor A	0.002303	<	0.01	significant
Factor B	0.000715	<	0.01	significant
Interaction of A and B	0.672177	>	0.1	Not significant

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