Question

coatings are being considered for corosion puotection of metal pipe. The pipe will be buried in three different types of soil. To investigate whether the amount of corrosion depends either on the coating or on the type of soil, 24 pieces of pipe are selected. Each piece is coated with one of the four coatings and buried in one of the three types of soil for a fixed time, after which the amount of corrosion is deternined. The data appears in the table. Coating (Factor A) Corrosion Amount 1 56, 59 53, 5570$1, 55 Soil Type (Factor B) 2 49, 0 S1,52 49, 46 48,47 3 50, 56 51,50 50, 5452, 56 0 Complete two-way ANOVA table. (1 point) MS DF 3.35 Coating (A) Soil (B) Coating Soil Error Total 68.083 4.9583 257.958 B. State and conclude test for the relevant hypotheses at significance level a -0.05. (2 points)

Answer 1

ODF c oar in Coaina- SDFcoasing Soil 4 Totok SDF Er23-3+2+6)12 sem -59-4994 ①SScoaring: MSCoaring -5.5367 rro EYror ERTOY Coatina - D F coati n Coatina. - MS soil F s Soil - - 2-62 413 すČemple t o :Way ANOVA table: F Source DF 3 2 124.838구 62-4123 25-17 6 68 083 341 2.28 12 59.49% .49583- MS 3.35 16,'103 Б. 53 67 Coating (A) Soil (8)2 C S Eryor Tota23 257.958

Population standard deviation , σ 0.28 sample size, n= 12 Sample mean, X5.25 For 95% confidence, significance lev .. Critical value , 군%,- el,d 1-0.95-0.05 0-0251 60 (tio-tailed 0.2 5.235 -1 960 - 5-657 51166 0.28 5.215 +1.960 Upper limit - X+ s 5.433 42 5. 4334 (3) coaing (A)-starstic35 Cviical Value, F o, 3,12 3 49 As the F-Statistic doen not exceed the cvihica value, we oil to veject the wail hpothanis and conclude the voriable coating (A) is nat signi icant Soil (B):. F Statistic-2517 As the F-stai sHe enceeds the citical value, we veject the nu hypothais and conelude. the variable soil (B)' is igniticn Inreriacrien (Coasimsoil) F-stat- 2.20 evitical vlue Fos, 6,11- - 299 As he F-staitie doen not exceed he criHca alue, we fail to veject the nul hwpothais and conclude thor he mteractionf he ho variable s not siamificant