Question

2. Managers of a transit system want to evaluate four types of tires with respect to wear. Three buses are being used for a test drive with one tire of each type placed randomly on the four wheels of each bus. The tread wear in millimeters 3hj for tire type J installed on bus i is measured after 1000 miles. The data are given in the table below Tire type j Bus 23 4 9.1 17.1 20.8 11.8 13.4 20.3 28.3 16 15.6 24.6 23.7 16.2 2 3 (a) Compute the total sum of squares (SST), the sum of squares representing the dif- ferences between tire types (SSM), and the residual sum of squares (SSE) (b) Perform the one-way ANOVA F-test for the difference of wear between tire types using the critical value approach. What can the managers conclude about the four types of tires just based on this test?

Answer 1

data

tire 1	tire 2	tire 3	tire 4
9.1	17.1	20.8	11.8
13.4	20.3	28.3	16
15.6	24.6	23.7	16.2

Using Excel

Anova single factor

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
tire 1	3	38.1	12.7	10.93
tire 2	3	62	20.66667	14.16333
tire 3	3	72.8	24.26667	14.30333
tire 4	3	44	14.66667	6.173333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	256.6825	3	85.56083	7.510277	0.01031	4.066181
Within Groups	91.14	8	11.3925
Total	347.8225	11

a)

SST = 347.8225

SSM + 256.6825

SSE = 91.14

b)

F = 7.5103

p-value = 0.0103

p-value < alpha(0.05)

hence we reject the null hypothesis

we conclude that there is significant difference of wear between tire types