Question

The article "Origin of Precambrian Iron Formations" (Econ. Geology, 1964: 1025–1057) reports the following data on total Fe for four types of iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 = hematite). 1: 2: 20.5 25.2 26.3 34.0 29.5 26.2 36.5 33.1 28.1 27.8 25.3 27.1 24.0 26.2 17.1 26.8 34.0 27.5 29.9 29.5 44.2 34.1 34.1 32.9 27.0 20.5 20.2 23.7 29.4 30.0 30.3 36.3 28.0 31.3 23.7 24.9 27.9 35.6 31.4 25.5 3: 4: Carry out an analysis of variance F test at significance level .01, and summarize the results in an ANOVA table.

Answer 1

solution The aim is to compute analysis of variance, ve Fitest J-16 biven, I = 4 Let true uy be the formation of average total F, (i=1,2,3,4) Null hypothesi's Ho : M = M₂ = M₂ = 14 is lu that Same the for all This implies four types Alternate hypothesis - Ha i at least one of is different mean freedom for treatments is Degrees of (1-1)=14-) =3 for error is free dom of Degrees 36 - 40-4 (n-1) critical value for the rejection The F (from excel region is 24.38 F.01,3136 Anchon = F.INV.RT (0.01, 3, 361) four treatments as follows: Sum of the 246.9 X2 299.5 = 260.8 338.4 X4 = each of the 40 and square Summing obseovations the following to obtain

RSS = EEX ij [(2015) + (28.1)+ +(25-5)?] 33882.24 Raw Sum of squares - Total Sulm of squares correchón factor TSS = (2 *): RSS n - 33882.24 32809.98 - 1072.26 due to treatment Sum of the Squares is follows: ag CÊ X;)? - SST, Ś (Ex;'): n I 10 (333191.1) - 32809.98 33319:11 - 32809.98 509.126 is compute ed of Squares Sum Eroor follows: SSE ISS SSTO 509.126 : 1072. 26 2 563.134 of squares due to treatments Mean Sum is follows: cus

MST SSTO I-1 509.126 3 - 169.7) Mean sum of Squares enors due is as follows: SSE MSE - n-I 563.134 40 - 4 563.134 36 215.64 MST Now, compute the test Stab'so'c, f. MSE MSTO 169.71 10. 85 15.84 MSE the values ANOVA table, is substitute follows: as df Sum of Squares Source of variation Mean Square F 509.126 169.71 3 10.85 Treatments 563.134 15.64 36 Error 1072.26 39 Total

The value 0.000032 excel (From since the of for Р FO-01,3,36 is fan chon F.DIST.RT(10.85, 3, 36)) value of less than significance 0:01 the null hypothesis 'p' is the level of Reject there is a Therefore, conclude that significant difference four types of iron between 911 the formation. please like & support. Thank you.