The article “An Investigation of the CaCO3-CaF2-K2SiO3- SiO2-Fe Flux System Usin

Question

     The article “An Investigation of the CaCO3-CaF2-K2SiO3-

SiO2-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.

Can we conclude that there are differences in the population means among the four flux types?

Hints:

1)    Only one factor- Flux type is considered

2)    Assume equal variances

3)    Use ANOVA to solve

Flux Sample Mean .8 263.2 271.0 262.0 Sample standard Devlation 9.7570 5.4037 8.7178 7.4498 Sample Values 250 264 256 260 239 C 257 279 269 273 277 D 253 258 262 264 273 264 273

Explanation / Answer

H0: All the four treatment means are equa

H1: Atleast one treatment means is not equal

alpha:5%

Test statistic:

Anova Tale

F cal=3.87

COnclsuion:

P value=0.029 <0.05 we reject the null hypothesis.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 5 1269 253.8 95.2 B 5 1316 263.2 29.2 C 5 1355 271 76 D 5 1310 262 55.5 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 743.4 3 247.8 3.873388 0.029437 3.238872 Within Groups 1023.6 16 63.975 Total 1767 19

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