Question

As part of a study designed to compare hybrid and similarly equipped conventional vehicles, a group tested a variety of classes of hybrid and all-gas model cars and sport utility vehicles (SUVs). Suppose the following data show the miles-per-gallon rating 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.

Class	Type	MPG
Small Car	Hybrid	36
Small Car	Conventional	29
Small Car	Hybrid	43
Small Car	Conventional	33
Midsize Car	Hybrid	28
Midsize Car	Conventional	22
Midsize Car	Hybrid	33
Midsize Car	Conventional	24
Small SUV	Hybrid	27
Small SUV	Conventional	21
Small SUV	Hybrid	28
Small SUV	Conventional	22
Midsize SUV	Hybrid	23
Midsize SUV	Conventional	19
Midsize SUV	Hybrid	24
Midsize SUV	Conventional	18

At the α = 0.05 level of significance, test for significant effects due to class, type, and interaction.

Find the value of the test statistic for class. (Round your answer to two decimal places.)___

Find the p-value for class. (Round your answer to three decimal places.)

p-value = ____

State your conclusion about class.

Because the p-value ≤ α = 0.05, class is significant.

Because the p-value > α = 0.05, class is not significant.    

Because the p-value ≤ α = 0.05, class is not significant.

Because the p-value > α = 0.05, class is significant.

Find the value of the test statistic for type. (Round your answer to two decimal places.)___

Find the p-value for type. (Round your answer to three decimal places.)

p-value = ____

State your conclusion about type.

Because the p-value > α = 0.05, type is not significant.

Because the p-value > α = 0.05, type is significant.    

Because the p-value ≤ α = 0.05, type is significant.

Because the p-value ≤ α = 0.05, type is not significant.

Find the value of the test statistic for interaction between class and type. (Round your answer to two decimal places.)___

Find the p-value for interaction between class and type. (Round your answer to three decimal places.)

p-value = ____

State your conclusion about interaction between class and type.

Because the p-value ≤ α = 0.05, interaction between class and type is significant.

Because the p-value > α = 0.05, interaction between class and type is significant.    

Because the p-value ≤ α = 0.05, interaction between class and type is not significant.

Because the p-value > α = 0.05, interaction between class and type is not significant.

Answer 1

The two factors ANOVA with replication analysis is performed in excel by following these steps,

Step 1: Write the data values in excel. The screenshot is shown below,

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

Step 3: Select Input Range: All the data values column, Rows per Sample: 2, Alpha = 0.05. The screenshot is shown below,

The result is obtained.  The screenshot is shown below,

Class

test statistic for class (F-statistic) = 147.08
p-value for class = 0.000
conclusion: Because the p-value ≤ alpha = 0.05, class is significant.

Type

test statistic for type (F-statistic) = 29.76
p-value for type = 0.000
conclusion: Because the p-value ≤ alpha = 0.05, type is significant.

interaction between class and type

test statistic for interaction (F-statistic) = 0.39
p-value for interaction = 0.761
conclusion: Because the p-value > alpha = 0.05, interaction between class and type is not significant.