Question

In an experiment to see whether the amount of coverage of light-blue interior latex paint depends either on the brand of paint or on the brand of roller used, one gallon of each of four brands of paint was applied using each of three brands of roller, resulting in the following data (number of square feet covered).

Roller Brand

1 2 3

  1 454 445 451

Paint 2 446 442 446

Brand 3 439 441 444

4 444 437 443

(a) Construct the ANOVA table. [Hint: The computations can be expedited by subtracting 400 (or any other convenient number) from each observation. This does not affect the final results.] (Round your answers to two decimal places.)

Source df SS MS f F0.05

Paint Brand

Roller Brand

Error

Total

(b) Test hypotheses appropriate for deciding whether paint brand has any effect on coverage. Use α = 0.05.

State the appropriate hypotheses. H0A: α1 ≠ α2 ≠ α3 ≠ α4 HaA: all αi's = 0 H0A: α1 = α2 = α3 = α4 = 0 HaA: at least one αi ≠ 0 H0A: α1 = α2 = α3 = α4 = 0 HaA: no αi = 0 H0A: α1 ≠ α2 ≠ α3 ≠ α4 HaA: at least one αi = 0 What can you conclude? Reject H0. The data does not suggest that paint brand has an effect. Fail to reject H0. The data suggests that paint brand has an effect. Reject H0. The data suggests that paint brand has an effect. Fail to reject H0. The data does not suggest that paint brand has an effect.

(c) Repeat part (b) for brand of roller. State the appropriate hypotheses. H0B: β1 ≠ β2 ≠ β3 HaB: all βj's are equal H0B: β1 = β2 = β3 = 0 HaB: no βj = 0 H0B: β1 = β2 = β3 = 0 HaB: at least one βj ≠ 0 H0B: β1 ≠ β2 ≠ β3 HaB: at least one βj = 0 What can you conclude? Fail to reject H0. The data does not suggest that roller brand has an effect. Reject H0. The data suggests that roller brand has an effect. Reject H0. The data does not suggest that roller brand has an effect. Fail to reject H0. The data suggests that roller brand has an effect.

(d) Use Tukey's method to identify significant differences among paint brands. (Round your answer to two decimal places.)

w =

Which means differ significantly? (Select all that apply.) x1. and x2. x1. and x3. x1. and x4. x2. and x3. x2. and x4. x3. and x4. There are no significant differences.

Is there one brand that seems clearly preferable to the others? Paint Brand 1 Paint Brand 2 Paint Brand 3 Paint Brand 4 None of the brands is clearly preferable to the others You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

a)

Source of Variation	SS	df	MS	F-stat		F-critical
paint brand	150.67	3	50.22	8.18		4.76
Roller brand	57.17	2	28.58	4.66		5.14
Error	36.83	6	6.14
Total	244.67	11

b)

H0A: α1 = α2 = α3 = α4 = 0 HaA: at least one αi ≠ 0

Reject H0. The data suggests that paint brand has an effect.

c)

H0B: β1 = β2 = β3 = 0 HaB: at least one βj ≠ 0

Fail to reject H0. The data does not suggest that roller brand has an effect.

d)

Level of significance	0.05
no of treatments	4
df error	6
MSE	6.1389
q-statistic value	4.8956

W = critical value = q*√(MSE/2*(1/ni+1/nj)) = 7.00

if absolute difference of means > critical value,means are significnantly different ,otherwise not                      
answer:

paint 1 and paint 3

paint 1 and paint 4