An IE is studying the effectiveness of three methods (A, B and C) for assembling
ID: 3301815 • Letter: A
Question
An IE is studying the effectiveness of three methods (A, B and C) for assembling an electronic device. Each method is tested on two products as given below: (a) Give y_22 = ?, y_2. = ? y..= ? (b) Develop the analysis of variance (ANOVA) table and answer the question: does the method affect the assembly time at alpha = 0.05? (c) Give the statistical model for the response data and estimate all model parameters mu, tau + i (i = 1, 2, 3) and sigma^2 the variance of the time. (d) If the time is "smaller the better", what method is the best design and why? (e) Construct a contrast to test the hypothesis: H_0: mu_1 + mu_2 = 2 mu_3: another contrast to test the hypothesis H_0: mu_1 = mu_2. (f) Are these two contrasts orthogonal or not and why? (g) Find the sums of squares for them the test the hypothesis at alpha = 0.05.Explanation / Answer
(a) y22 = (14,12)
y2.=14+12=26
y.. = 78
(b)
No, the method does not affect the assembly time at 0.05.
SUMMARY Count Sum Average Variance Row 1 2 31 15.5 0.5 Row 2 2 26 13 2 Row 3 2 21 10.5 0.5 Column 1 3 41 13.66667 6.333333 Column 2 3 37 12.33333 6.333333 ANOVA Source of Variation SS df MS F P-value F crit Rows 25 2 12.5 75 0.013158 19 Columns 2.666667 1 2.666667 16 0.057191 18.51282 Error 0.333333 2 0.166667 Total 28 5