Question

A car dealership would like to test the hypothesis that a difference exists in the city gas mileage (miles per gallon when driven in the city) of three cars, Honda Insight, Hyundai Ioniq and Toyota Camry. The following data represent the miles per gallon for a random sample of Honda Insight, Hyundai Ioniq and Toyota Camry cars.

Honda Insight	Hyundai Ioniq	Toyota Camry
40	35	35
36	37	34
37	38	31
38	34	36
38	34	33
36	36	35

Use Excel to perform a one-way ANOVA and state your conclusion using α = 0.05.

Answer 1

Ans:

	Group 1	Group 2	Group 3	Total
Sum	225	214	204	643
Count	6	6	6	18
Mean, Sum/n	37.5	35.66667	34
Sum of square, Ʃ(xᵢ-x̅)²	11.5	13.33333	16
Standard deviation	1.517	1.633	1.789

Number of treatment, k =	3
Total sample Size, N =	18
df(between) = k-1 =	2
df(within) = N-k =	15
df(total) = N-1 =	17
SS(between) = (Sum1)²/n1 + (Sum2)²/n2 + (Sum3)²/n3 - (Grand Sum)²/ N =	36.7778
SS(within) = SS1 + SS2 + SS3 =	40.8333
SS(total) = SS(between) + SS(within) =	77.6111
MS(between) = SS(between)/df(between) =	18.3889
MS(within) = SS(within)/df(within) =	2.7222
F = MS(between)/MS(within) =	6.7551
p-value = F.DIST.RT(6.7551, 2, 15) =	0.0081

ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	36.7778	2	18.3889	6.7551	0.0081
Within Groups	40.8333	15	2.7222
Total	77.6111	17

Null and Alternative Hypothesis:
Ho: µ1 = µ2 = µ3
H1: At least one mean is different.
Test statistic:
F =	6.7551
Critical value:
Critical value Fc = F.INV.RT(0.05, 2, 15) =	3.6823
p-value:
p-value = F.DIST.RT(6.7551, 2, 15) =	0.0081
Decision:
P-value < α, Reject the null hypothesis.

Conclusion:There is sufficient evidnece to conclude that there is a significant difference in the city gas mileage (miles per gallon when driven in the city) of three cars, Honda Insight, Hyundai Ioniq and Toyota Camry.