Question

Three different brands of tires were compared for wear characteristics. For each brand of tire, ten tires were randomly selected and subjected to standard wear testing procedures. The average mileage obtained for each brand of tire and sample standard deviations (both in 1000 miles) are shown below.

	Brand A	Brand B	Brand C
Sample Size	10	10	10
Average Miles (x)	37	38	33
Sample St. Deviation	3	4	2

(a) State the null and alternative hypotheses to see if the mean mileage for all three brands of tires is the same.

(b) Find the overall sample mean (x ), overall sample size ( T n ), and the number of treatments (k).

(c) Compute the sum of squares between treatments (SSTR) and the sum of squares due to error (SSE). Show your complete work.

(d) Carry out the analysis of variance procedure for a completely randomized design by completing the ANOVA table.

Source	D.F.	S.S.	M.S.	F

(e) Compute the p-value. At the 1% level of significance, can you reject the null hypothesis in part (a)? Explain. What conclusion can you draw in this context?

(f) Use Fisher's LSD procedure to determine which mean (if any) is different from the others. Use  = 0.05.

Answer 1

H0 : There is no difference in mean mileage of all the three brands of tires.

H1 : There is significant difference in mean mileage of all the three brands of tires.

		Brand A	Brand B	Brand C	total
	SAMPLE SIZE	10	10	10	30
	AVERAGE MILEAGE	37	38	33	1080/30 = 36
	total	370	380	330	1080
	S.D.	3	4	2

Overall sample mean = 1080/30 = 36

Overall sample size = 10 +10 +10 = 30

SS df MS F p

Between:     140.000 2 70.000 7.241    0.003

Within:        261.000 27 9.667          

Total:           401.000 29               

If the P-value(0.003) is less than α (0.01), reject the null hypothesis.

Brand A vs Brand B: Diff=1.0000, 99%CI=-3.4193 to 5.4193, p=0.7544

Brand A vs Brand C: Diff=-4.0000, 99%CI=-8.4193 to 0.4193, p=0.0205

Brand B vs Brand C: Diff=-5.0000, 99%CI=-9.4193 to -0.5807, p=0.0035