Math 687 Exam II Solutions, Spr04.

# Design and Analysis of Experiments, 5th Edition

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- ,-1 ~ ffltn E.r";;~ 1. (75 pts.) A balanced 22 factorial design was used to see how the factors Temperature (A) and Copper content (B) effect the warping of metallic plates 1. The high level of temperature was 100° C and the low level of temperature was 50° C. The high level of copper content was 80% and the low level was 40%. The response variable was a measure of the amount of warping (larger values correspond to greater warping). A B AB Temperature Copper Observations Total Mean SD Content (Warping) (1) -1 -1 +1 17 20 37 18.5 2.1 ~I a +1 -1 -1 16 12 28 14.0 2.8 'L b -1 +1 -1 24 22 46 23.0 1.4 \$3 ab +1 +1 +1 25 23 48 24.0 1.4 7, a. Estimate the (main) effect A -~~_.i.-~-= -~-~-~ ~ = -~~ ~2 , - 4 b 4- -.1-1 = - J. 7 .5 n 2 k"-\ 1- b. Estimate the (main) effect B - ~ ,) - ~ h ~ 4; ~ -::. - ~~-=-~~~.-!~..:_!~ .:= 7 . 'l .s ~ 2.k~\ 4- c. Estimate the (interaction) effect AB ~- ~-- b .J- 41- -:: ~=-~3- '1 ,",.f- 1~ = 2.75 !I12.k'" 1- d. Estimate 0", the assumed common standard deviation of ~ measurement of warping. ~l. - 5,'2...,... 5; ~.5~""'" 5,'1. - (211)'t.,.f- (z.S)'Z.-+- Q.1-)1 (,,'1)' vp- - -- .q. 4- ~ ~p C; 2.o( e. Estimate the standard deviation of ~ ~. (\ - r - .J... ) 0- 0-"'" 51) (~I, = --- = - ~ ~ ::: 1.4-'2'2. ~~ Vi: This is a subset of the datadisplayed in Johnson and Leone (1977), Statistics and Experimental Designin Engineering and the Physical Sciences, John Wiley, New York, NY. 2 ~"~,.,,.,.., y~~~,c"""-.,,. ,.,

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