Question

P. Turnpike	MF. Expressway	BV. Expressway
7	10	1
14	1	12
32	1	1
19	0	9
10	11	1
11	1	11

A state employee wishes to see if there is a significant difference in the number of employees at the interchanges of three state toll roads. The data are shown. At α=0.10, test the claim that there is no difference in the average number of employees at each interchange.

Answer 1

	P. Turnpike	MF. Expressway	BV. Expressway	Total
Sum	93	24	35	152
Count	6	6	6	18
Mean, Sum/n	15.5	4	5.8333
Sum of square, Ʃ(xᵢ-x̅)²	409.5	128	144.8333

Null and Alternative Hypothesis:

Ho: µ1 = µ2 = µ3

H1: At least one mean is different.

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 = 458.1111

SS(within) = SS1 + SS2 + SS3 = 682.3333

SS(total) = SS(between) + SS(within) = 1140.4444

MS(between) = SS(between)/df(between) = 229.0556

MS(within) = SS(within)/df(within) = 45.4889

F = MS(between)/MS(within) = 5.0354

Critical value Fc = F.INV.RT(0.1, 2, 15) = 2.695

Decision:

As F = 5.0354 > 2.695, Reject the null hypothesis.

There is enough evidence to reject the claim that there is no difference in the average number of employees at each interchange.

ANOVA
Source of Variation	SS	df	MS	F
Between Groups	458.1111	2	229.0556	5.0354
Within Groups	682.3333	15	45.4889
Total	1140.4444	17