Three different brands of tires were compared for wear characteristics. For each
ID: 3270466 • Letter: T
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. (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 (n_T), 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. (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 alpha = 0.05.Explanation / Answer
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 (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
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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
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