Question

The Department of Energy and the U.S. Environmental Protection Agency's 2012 Fuel Economy Guide provides fuel efficiency data for 2012 model year cars and trucks.† The file named CarMileage provides a portion of the data for 309 cars. The column labeled Size identifies the size of the car (Compact, Midsize, and Large) and the column labeled Hwy MPG shows the fuel efficiency rating for highway driving in terms of miles per gallon. Use α = 0.05 and test for any significant difference in the mean fuel efficiency rating for highway driving among the three sizes of cars. (Hint: you will need to re-organize the data to create indicator variables for the qualitative data).

State the null and alternative hypotheses.
H₀: β₁ = β₂ = 0
H_a: One or more of the parameters is not equal to zero.

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

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

p-value =

please explain the process through excel

Size	Hwy MPG
Compact	30
Compact	31
Compact	31
Compact	33
Compact	29
Compact	31
Compact	27
Midsize	33
Midsize	34
Midsize	32
Midsize	30
Midsize	31
Midsize	30
Large	34
Large	34
Large	34
Large	35
Large	35
Large	28
Large	25
Large	25
Large	27
Large	27
Large	31
Large	27

Answer 1

First of all, we need to reorganize the data to distinguish each column, the size of the cars with their mileage is reflected. I shall name the three columns as Compact, midsize and Large. Under each column, the mileage information will be entered or copied. The data will now look like this:

Compact	Midsize	Large
30	33	34
31	34	34
31	32	34
33	30	35
29	31	35
31	30	28
27		25
		25
		27
		27
		31
		27

Now Compact column will have 7 rows of data and Midsize will have 6 and Large will have 12 rows.

Null Hypothesis: The average mileages of all three sizes are the same

Where is the Average for compact size car, is the average of mid sized cars and is the average of the Large sized cars.

Alternative Hypothesis: One or more of the parameters is not equal

Test Statistic : where MSS is Mean Sum of squares from ANOVA table and Bet refers to between groups and Err refers to Error or Within groups. In the output, p-values will also be reported.

We shall now proceed to analysis using Excel. Under Excel, use the data analysis tool. Under the tool, use Anova: Single factor. In this option, select the options grouped by Columns and Click the Labels in first row option and give a range to output. We shall get the following output.

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Compact	7	212	30.28571	3.571429
Midsize	6	190	31.66667	2.666667
Large	12	362	30.16667	16.33333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	9.731429	2	4.865714	0.499214	0.613719	3.443357
Within Groups	214.4286	22	9.746753
Total	224.16	24

From the table above, the test statistics is 0.50 and the p-value is 0.61.