QUESTION 1 The article \"An Investigation of the CaCO3-CaF2-K2SiO3-Si02-Fe Flux

Question

QUESTION 1 The article "An Investigation of the CaCO3-CaF2-K2SiO3-Si02-Fe Flux System Using the Submerged Arc Welding Process on HSLA-100 and AISI-1081 Steels (G Fredrickson, M.S. Thesis, Colorado School of Mines, 1992) describes an experiment in which welding fluxes with differing chemical compositions were prepared Several welds using each flux were made on AISI-1018 steel base metal.The results of hardness measurements, on the Brinell scale, of five welds using each of four fluxes are presented in Table below. Assume equal variances and level of significance =0.05. Hint only one factor ie. flux type is considered. Use 4DP for all your answers Sample Standard Deviation Sample Flux Sample Values Mean 250 264 256 260 239 253.8 B 263 254 267 265 267 263.2 C 257 279 269 273277 271.0 9.7570 5.4037 8.7178 D253 258 262 264 273 2620 74498 Ho and H1 are stated as H1 : not all , are equal a. SSA = b. MSA c. F test statistic Fstat d. Critical value Fadf1.df2 = e. p-value f. Decision: we (You may use R or data analysis tool in Excel to find the p-value) (ill in the blank by "should" or "should not") reject the null hypothesis

Explanation / Answer

from above data:

a)SSA=743 ; SSW =1023.5943

b) MSA =371.7000 ; MSW =60.2114

c) Ftest statsiic =6.1732

d) crtiival value =3.5915

e) p value =0.0097

f) we should reject

i ni Xi Si^2 ni*(Xi- grand mean)^2 (ni-1)*Si^2 A 5 253.8 95.199 378.450 380.796 B 5 263.2 29.200 2.450 116.800 C 5 271 76.000 361.250 304.000 D 5 262 55.500 1.250 221.998 Weighted mean 262.500 743.400 1023.594 SSG SSE Source of variation SS df MS F P value treatment 743.400 2 371.700 6.173 0.0097 error 1023.594 17 60.211 total 1766.994 19

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