The article \"An Investigation of the CaCO3-CaF2-K2SiO3- SiO2-Fe Flux System Usi

Question

The article "An Investigation of the CaCO3-CaF2-K2SiO3- SiO2-Fe Flux System Using the Submerged Are 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.

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu1 = mu2 = mu3 = mu4

H1 : Atleast one of the mean is differ than 0.

Assume alpha = 5% = 0.05

Four means we can test using ANOVA.

ANOVA in EXCEL :

steps :

Enter data in EXCEL sheet --> Data --> Data Analysis --> Anova : Single Factor --> ok --> Input Range : select all data range --> Grouped by : columns --> Alpha : 0.05 --> Output Range : select one empty cell --> ok

Results :

Test statistic F = 3.873

P-value = 0.03

P-value < alpha

Reject H0 at 5% level of significance.

Conclusion : Atleast one of the mean is differ than 0.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 5 1269 253.8 95.2 Column 2 5 1316 263.2 29.2 Column 3 5 1355 271 76 Column 4 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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