420Hw10ans - STAT 420 (10 points) (due Friday, November 9,...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 420 Fall 2007 Homework #10 (10 points) (due Friday, November 9, by 3:00 p.m.) 1. An engineer is investigating the strength of concrete beams made from four types of cement and employing three curing processes. The breaking strengths are measured and are presented below. Curing Cement Type Process A B C D 1 14 6 22 10 2 15 8 20 7 3 10 7 18 7 a) List an appropriate model and the underlying assumptions for this situation. b) Construct the ANOVA table and test for differences in cement types and curing processes. Assume a 5-percent significance level. a) Y i j = μ + α i + β j + ε i j , i = 1, 2, 3, j = 1, 2, 3, 4, α 1 + α 2 + α 3 = 0, β 1 + β 2 + β 3 + β 4 = 0, ( Curing Process ) ( Cement Type ) ε i j are independent N ( 0, σ 2 ) random variables. b) > Str <- c(14, 6,22,10,15, 8,20, 7,10, 7,18, 7) > Cur <- c( 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3) > Cem <- c( 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4) > > summary(aov(glm(Str ~ factor(Cur) + factor(Cem)))) Df Sum Sq Mean Sq F value Pr(>F) factor(Cur) 2 14.00 7.00 2.625 0.1517037 factor(Cem) 3 318.00 106.00 39.750 0.0002361 *** Residuals 6 16.00 2.67 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
OR Curing CementType Process A B C D Mean 1 14 6 22 10 13 2 15 8 20 7 12.5 3 10 7 18 7 10.5 Mean 13 7 20 8 12 SS
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

Page1 / 6

420Hw10ans - STAT 420 (10 points) (due Friday, November 9,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online