3. The data set “Miles per Gallon\" in Table 913 gives the average high- way mil

Question

3. The data set “Miles per Gallon" in Table 913 gives the average high- way mileage per gallon (MPG) of gasoline for a random sample of minivans, mid-size cars, and SUVs by make. a. TABLE 9.13 Miles Per Gallon" Data Set Conducta one-way ANOVA to determine whether the mean high- way MPG differs among minivans, mid-size cars, and SUVs. What assumption ence about the difference in the mean MPG among minivans mid-size cars, and SUVs? Using both exploratory analyses and formal tests, establish whether these assumptions have been rea- sonably met Do the data provide sufficient evidence to indicate that there is a difference in the mean MPG a SUVs? Justify your response. Minivan Mid-size SUV Brand 1 Brand 1 Brand 1 Brand 1 Brand 1 Brand 1 Brand 2 Brand 2 Brand 2 Brand 2 Brand 2 Brand 2 Brand 3 Brand 3 Brand 3 Brand 3 Brand 3 Brand 3 b. s need to be met in order to make a valid infer- c. 18 18 18 18 18 mong minivans, mid-size cars, and 21 21 21 21 21 18

Explanation / Answer

Given

ANOVA table

Sum of squares of all the elements

SS = 20^2 + 19^2 + .... + 17^2 = 21946

Q =

SS - T^2/n = 21946 - 1080^2/54 = 346

Q1 = (Ti^2/ni) - T^2/n

= 21702.78 - 1080^2/54 = 102.78

Q2 = Q - Q1

= 346 - 102.78

= 243.22

For M.S = S.S/ df

df between brands = h-1 = 3-1 = 2

The F value is higher than the critical value at (v1 = 2, v2 = 50) is

at 0.05 level

3.18

There exists significant difference between all the 3 cars

Also, before conducting this test,

we need to priliminary test

1) Is the brand number impacting the value

Select all brand values and conduct a test between them

If the result has no significant difference than solving the above problem by one-way ANOVA analysis is apt.

Minivan Mid-size SUV Make 20 25 24 Brand 1 19 25 24 Brand 1 19 25 24 Brand 1 19 24 23 Brand 1 18 24 22 Brand 1 18 24 22 Brand 1 18 22 22 Brand 2 18 22 21 Brand 2 18 21 21 Brand 2 18 21 21 Brand 2 18 21 21 Brand 2 18 19 20 Brand 2 18 19 20 Brand 3 18 18 20 Brand 3 17 18 19 Brand 3 17 18 17 Brand 3 17 17 17 Brand 3 17 17 17 Brand 3 SUM Ti 325 380 375 1080= T ni 18 18 18 54 = N Ti^2/ni 5868.06 8022.22 7812.5 21702.78

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