Question

1. A research team wishes to specify a manufacturing process so that Y, the area in a product affected by surface flaws is as small as possible. They have four levels of concentration of a chemical used to wash the product before the final manufacturing step and want to determine whether the concentration level causes a change in E(Y). They run a balanced one-way layout with 6 observations for each concentration with level 1 set at 10%, level 2 set at 15%, level 3 set at 20%, and level 4 set at 25%. They run a balanced one-way layout with 6 observations for each treatment. They observe that Vi = 264.5, y2 = 255.9, yz = 216.2, and y. = 263.8, where y, is the average of the observations taken on the ith level. They also observe that si = 411.9, sa = 522.2, s= 631.8, and si = 521.9, where s is the unbiased estimate of the variance for the observations taken on the ith level. a. Complete the analysis of variance table for these results; that is, be sure to specify the degrees of freedom, sum of squares, mean square, and F-test. b. What is your conclusion? Use significance levels set to 0.10, 0.05, and 0.01. Make sure that you discuss the optimal setting of the concentration level and how Vou could document it. L i te lir

Answer 1

A)

Hypothesis:

H0: $\mu 1=\mu 2=\mu 3$

H1: Not H0

ANOVA table

source of variation	sum of squares	d.f	M.S.S	F	p
Between grp	9467.4	3	3155.8	0.0113	0.9983
Within grp	5569526.5	20	278476.3
total	5578993.9	23

here

Decision rule:

Reject H0 If F>F((k-1),(N-k))

F>F(4,20)

0.0113<2.2489

also using P-value 0.9983>0.05 so there is no difference we accept H0

so accept H0 so there is no statistically significant difference

Conclusion:

The concentration level of the four chemicals is the same.