Question 1

1. 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. Assume equal variances and level of significance α=0.05. Hint: only one factor i.e. flux type is considered. Use 4DP for all your answers.

   Flux	Sample Values					Sample Mean	Sample Standard Deviation
   A	250	264	256	260	239	253.8	9.7570
   B	263	254	267	265	267	263.2	5.4037
   C	257	279	269	273	277	271.0	8.7178
   D	253	258	262	264	273	262.0	7.4498

   
   H ₀and H ₁are stated as: H0: μ ₁= μ ₂= μ ₃= μ _{4 H1:}not all µ _jare equal
   

   1. SSA = Blank 1 , SSW = Blank 2
   2. MSA = Blank 3 ,MSW = Blank 4
   3. F test statistic F _stat= Blank 5 .
   4. Critical value F _α,df1,df2= Blank 6
   5. p-value= Blank 7 (You may use R or data analysis tool in Excel to find the p-value)
   6. Decision: we Blank 8 (fill in the blank by " should" or " should not") reject the null hypothesis.

      Question 2

      1. A study is made of the effect of curing temperature on the compressive strength of a certain type of concrete. Five concrete specimens are cured at each of four temperatures, and the compressive strength of each specimen is measured(in MPa). The results are as follows:

         Temperature (C 0)	Strengths (MPa)
         0	31.2	29.6	30.8	30.0	31.4
         10	30.0	27.7	31.1	31.3	30.6
         20	35.9	36.8	35.0	34.6	36.5
         30	38.3	37.0	37.5	36.1	38.4

         
         Assume equal variances and α=0.05. ANOVA analysis may be performed to check if the mean strength differs with temperature. Use 4DP for all your solutionsH ₀and H ₁are stated as: H0: μ ₁= μ ₂= μ ₃= μ ₄H1: not all µ _jare equal

         1. SSA = Blank 1 , SSW = Blank 2
         2. MSA = Blank 3 , MSW = Blank 4
         3. F test statistic F _stat= Blank 5 .
         4. Critical value F _α,df1,df2= Blank 6
         5. Decision: we Blank 7 (fill in the blank by " should " or " should not ") reject the null hypothesis.