Problem 3 0 an electronis device. Fach method is tested on two products as g (A,

ID: 3062221 • Letter: P

Question

Problem 3 0 an electronis device. Fach method is tested on two products as g (A, B and C) for Method Assembly Time (min 16 14 15 12 10 (a) Give y222, y-y.- (b) Develop the analysis of variance (ANOVA) table method affect the assembly time at -0.05? (c) Give the statistical model for the and answer the question: does the response data and estimate 0-1, 2, 3) and the variance of the time. (d) if the time is "smaller the better", what method is the best design and why? (c) Construct a contrast to test the hypothesis le 1-2us another contrast to test the all model parameters hypothesis!lo: ,-2. (t) Are these two contrasts orthogonal or not and why? (g) Find the sums of squares for them the test the hypothesis at a-0.05. 2 31 5.D.5 2 2 2 13 2 5 D. 5 65 Lows rror

Explanation / Answer

ANOVA: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

Method A

15.5

0.5

Method B

Method C

10.5

0.5

ANOVA

Source of Variation

P-value

F critical

Between Groups

12.5

0.035071

9.552094

Within Groups

Total

The given data is suitable for ONE WAY ANOVA.

b) Since the p-value of the ANOVA = 0.035071 < 0.05 implies that methods do differ significantly.

c) Statistical model for the data is as follows;

Yij = + i + ij where Yij is the jth response in ith method, i=1,2,3 and j=1,2.

– common effect

i – effect due to ith method

ij – Random errors ~ N(0,2)

Parameter estimates:

– Combined Mean = 13

1= Combined Mean – Mean of 1st Method = 13-15.5 = -2.5

2= Combined Mean – Mean of 2st Method = 13-13 = 0

3= Combined Mean – Mean of 3st Method = 13-10.5 = 2.5

2 = 1

d) “Smaller time is better” then method C is better than others, because its average time is least = 10.5

e) Contrast to test H0: 1 + 2 =23 is T1+T2-2T3 = 0

Contrast to test H0: 1 = 2 is T1 - T2 = 0

f) These two contrasts are orthogonal because sum of product of their respective coefficient is ZERO.