Question

The following data was reported on total Fe for four types of iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 = hematite).

The following data was reported on total Fe for four types of iron formation (1 = carbonate, 2 = silicate, 3 = magnetite, 4 = hemat 27.1 20.5 31.2 23.7 24.6 1: 20.8 28.1 27.8 27.0 28.2 25.2 25.3 2: 26.9 24.0 26.2 20.2 23.5 34.0 17.1 3: 30.4 34.0 27.5 29.4 28.1 26.2 29.9 4: 36.4 44.2 34.1 30.3 31.8 33.1 34.1 26.8 29.5 32.9 30.0 36.4 36.3 25.8 Carry out an analysis of variance F test at significance level 0.01. State the appropriate hypotheses. O Ho: M, uz M3 7 44 Ha: at least two u;'s are equal O Ho: My = Uz = uz = 44 Ha: at least two u;'s are unequal O Ho: 4, = 42 = uz = 44 Ha: all four u;'s are unequal O Ho: M, M27 M3 7 44 Ha: all four u;'s are equal Summarize the results in an ANOVA table. (Round your answers two decimal places.) Source df Sum of Squares Mean Squares Treatments Error Total Give the test statistic. (Round your answer to two decimal places.) f=

1:	20.8	28.1	27.8	27.0	28.2	25.2	25.3	27.1	20.5	31.2
2:	26.9	24.0	26.2	20.2	23.5	34.0	17.1	26.8	23.7	24.6
3:	30.4	34.0	27.5	29.4	28.1	26.2	29.9	29.5	30.0	36.4
4:	36.4	44.2	34.1	30.3	31.8	33.1	34.1	32.9	36.3	25.8

Carry out an analysis of variance F test at significance level 0.01. State the appropriate hypotheses.

H₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: at least two μ_i's are equalH₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: at least two μ_i's are unequal    H₀: μ₁ = μ₂ = μ₃ = μ₄
H_a: all four μ_i's are unequalH₀: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄
H_a: all four μ_i's are equal

Summarize the results in an ANOVA table. (Round your answers two decimal places.)

Answer 1

Hypothesis ] Ho; - M, =l2 =M3= My Vis Hai; - all four is are unequal. Consider = carbonate Ig- magnetite - silicate Y4=hematite. Til CS Scanned with CamScanner

Here given whene ic treatments) {= 1, 2, 3,4 j=1,2,..., 10 Cobs?) Here Tai = 261.2 I Taj 26.12 i J j 247 24.7 Y. Σ 10 301.4 = 30.14 Eg4j 339 10 33.9 T. SE Jij 1034.1 28.725 4X10 40 ..9.. = 28.73 Sum of ducto treatment =5.5.Tot S.S.Trt. (Ji.-J..)? in ja Lisis. Irt.= 514.7 sum of s. square due to Error =s.S.E.= S.S.E ICYjI ) ² = 563.6 Scanned with JH G Camscanner

S.S.Total = S.Stort t sis.E: sis.Ti = 517 7+ 563.6 = 108113 giren n=40 Wifi (Total) = n = 40-9=39 df (treatment) = K-1=4-1=3 d.f. (Error) ok= 400-4 = 36 - CS'Scale CamScanner

517 7 =172158 M.s.s.Trt = sisitot k-1 Mosis. Es S.S.E nok 563-3 15.66 36 14:56 = 11.02 Fratto - M.s.s.Tot M.S.S.E: ANONA Table Siv d.f. s.s. Tesis Faratio 3 Tot Errors S18. # 172.56 11.02 35 $63.3 15.66 Total. I 39 1081.3 Test Statistic Misis. Tot misis. Eo F = 172.56 11002 15.66 fcritical f Fikmi, n-ke), a = E3,36),0.01 -Cusing soft-ortable) Saared with

Decision Relle; - Reject Ho If GIF a critical F Here in these case CONF > critica .. Reject wo Ho at a cool lo's. Conclusion is all four Not same cal F means ie Middle & la talle CS Scanned with CamScanner

4:22 44 白83% 1% significance level Fol(19) - 2 4 5 6 7 | 8 9 10 V2 2 3 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 26 27 28 123456789p=28HS6282四引2345口%9如引见87%的如HR的死归%的加引见8外历历印%B5EBE 30 31 32 33 4052.19 4999.52 5403.34 5624.62 5763.65 5858.97 5928.33 5981.10 6022.50 6055.85 98.502 99,000 9.166 99.249 99.300 99.333 99,356 99.374 99.388 9.399 34.116 30.816 29.457 28.710 28.237 27.911 27,672 27.489 27.345 27.229 21.198 18,000 16.694 15.977 15.522 15.207 14.976 14.799 14.659 14.546 16.258 13.274 12.060 11.392 10.67 10.672 10.456 10.289 10.158 10.051 13.745 10.925 9,780 9.148 8.746 8.466 8.260 8.102 7,976 7.874 12.246 9,547 8.451 7.847 7,460 7.191 6.93 6.840 6.719 6.620 11.259 8.649 7.591 7.006 6.632 6.371 6.178 6.029 5.911 5.814 10.561 8,022 6,992 6.422 6,057 5.802 5.613 5.467 5.351 5.257 10.044 7.559 6.552 5.994 5.636 5.386 5. 200 5.057 4.942 4.849 9.646 7.206 6.217 5.668 5.316 5.06g 4,886 4.744 4.632 4.539 9.330 6.927 5.953 5.412 5,064 4.821 4,640 4.499 4.388 4.296 9,074 6.701 5.739 5.205 4,862 4.620 4.441 4.302 4.191 4.100 8.862 6.515 5.564 5.035 4.695 4.456 4.278 4.140 4.030 3.939 88.683 6.359 5.417 4.893 4.556 4.318 4.142 4.004 3.895 3.805 8.53] 6.226 5.292 4.773 4.437 4.202 4.026 3.890 3.780 3.691 8.400 6.112 5.185 4,662 4,336 4.102 3.927 3.791 3.682 3.593 8.285 6.013 5.092 4.579 4.248 4,015 3,841 3.705 3.7 3.508 8.185 5,926 5.010 4.500 4.171 3.939 3.765 3.631 3.523 3.434 8.096 5,849 4.938 4.431 4.103 3.871 3,699 3.564 3.457 3.368 8.017 5.780 4.874 4.369 4.042 3.812 3,640 3,506 3.398 3.310 7.945 5.719 4.817 4.313 3.98 3.758 3,587 3.453 3.346 3.258 7.88] 5,664 4,765 44.264 3.939 3.710 3,539 3.406 3,299 3.211 7.823 5.614 4.718 4.218 3.895 3.667 3.496 3.363 3,256 3.168 7.770 5.568 4.675 44.177 3.855 3.627 3.457 3.324 3.217 3.129 7.721 5.526 4,637 4.140 3.818 3.591 3.421 3.288 3.182 3.094 7.677 5.488 4.601 44.106 3.785 3.558 3.388 3.256 3.149 3.062 7.636 5.453 4,568 4.074 3.754 3.528 3,358 3.226 3.120 3.032 7.598 5.420 4.538 4.045 3.725 3.499 3,330 3.198 3.092 3.005 7.562 5.390 4.510 4.018 3,699 3.473 3,305 3.173 3.067 2.979 7.530 5.362 4.484 3.993 3.675 3.449 3,281 3.149 3.043 2.955 7.499 5.336 4,459 3.969 3,652 3.427 3.258 3.127 3.021 2.934 7.471 5.312 4,437 3.948 3.630 3.406 3.238 3.106 3,000 2.913 7.444 5,289 416 3.27 3.611 3.386 3.218 3.087 2.981 2.894 7.419 5.268 3.908 3,592 3.368 3,200 3.069 2.63 2,876 7.396 5.248 4.377 1.890 3.574 3.351 3.183 3.052 2.46 2.859 7.373 5.229 3.873 3.558 3.334 3.167 3.036 2.930 2.843 7.353 5.211 4.43 3.858 3.542 3.319 3.152 3.021 2.915 2.828 7.333 5.194 4.327 3.843 3,528 3.305 3.137 3.006 2.901 2.814 7.314 5.179 4.313 3.828 3.514 3.291 3.124 2.93 2,888 2.801 7.296 5.163 4.299 3.815 3.501 3.278 3.111 2.980 2,875 2.788 7.280 5.149 4.285 3.802 3.488 3.266 3,099 2.968 2.863 2.776 7.264 5.136 4.273 3.790 3.476 3.254 3,087 2.957 2,851 2,764 7.248 5.123 4,251 3.778 3.465 3.243 3,076 2.946 2.840 2.754 7.234 5.110 4.249 3.767 3.454 3.232 3,066 2.935 2,830 2,743 7.220 5.099 4.238 3.757 3.444 3.222 3,056 2.925 2,820 2.733 7.207 5.087 4.228 3.747 3.434 3.213 3,046 2.916 2.811 2.724 7.194 5,077 4.218 3.737 3.425 3.204 3,037 2.907 2,802 2.715 7.182 5,066 4.208 3.728 3.416 3.195 3.028 2.898 2.793 2.706 7.171 5,057 4.199 3.720 3.408 3.186 3.020 2.890 2.785 2.698 7.159 5,047 4.191 3.711 3.400 3.178 3,012 2.882 2.777 2.690 7.149 5,038 4.182 3.703 3.392 3.171 3,005 2.874 2.769 2.683 7.139 5,030 4.174 3.695 3.384 3.163 2.997 2.867 2.762 2.675 7.129 5,021 4.167 3.688 3.377 3.156 2.990 2.860 2.755 2.668 7.119 4.159 3.68] 3.370 3.149 2.983 2.853 2,748 2.662 7.110 5.006 4.152 3.674 3.363 3.143 2.977 2.847 2.42 2.655 7.102 4.998 4.145 3.667 3.357 3.136 2.971 2.841 2.736 2.649 7.093 4,991 4.138 3.661 3,351 3.130 2.65 2.835 2.730 2.643 7.085 4.984 4.132 3.655 3.345 3.124 2.959 2.829 2.724 2.637 7.077 4.977 4.126 3.649 3.339 3.119 2.953 2.823 2.718 2.632 7.070 4.971 4.120 3.643 3.333 3.113 2,948 2.818 2.713 2.626 7.062 4,965 4.114 3.638 3.328 3.108 2.942 2.813 2.708 2.62] 7.055 4.99 4.109 3.632 3.323 3.103 2.937 2.808 2.703 2.616 7.048 4.953 4.103 3.627 3.318 3.098 2.932 2.803 2,698 2.611 了自由了 17 anag 3677 2213 138 17日 763 1617 38 239 40 42 43 46 47 48 49 50 51 52 5.013 4 55 56 57 58 60 61 62 64 BE :::

- Minitab - Untitled Eile Edit Data Calc Stat Graph Editor Tools Window Help Assistant TOHO % *SOMO 2 += WITO BO GF -- ASK 2 Session X 7/30/2020 7:18:00 AM Descriptive Statistics: y1, y2, y3, y4 Variable y1 y2 y 3 y4 N 10 10 10 10 N* 0 0 0 0 Mean 26.12 24.70 30.140 33.90 SE Mean 1.05 1.41 0.954 1.50 StDev 3.33 4.46 3.016 4.75 Sum 261.20 247.00 301.400 339.00 Minimum 20.50 17.10 26.200 25.80 01 24.10 22.68 27.950 31.43 Median 27.05 24.30 29.700 33.60 Q3 28.13 26.83 31.300 36.32 Maximum 31.20 34.00 36.400 44.20 One-way ANOVA: y1, y2, y3, y4 Method Null hypothesis Alternative hypothesis Significance level All means are equal At least one mean is different a = 0.01 Equal variances were assumed for the analysis. Factor Information Factor Factor Levels 4 Values yi, y2, y3, y4 Analysis of Variance Source Factor Error Total F-Value 11.02 DF 3 36 39 P-Value 0.000 Seg ss 517.7 563.6 1081.3 Adj ss 517.7 563.6 Contribution 47.888 52.128 100.00% Adj MS 172.56 15.66 Model Summary S R-sq R-sq(adj) PRESS R-sq (pred) Activate Windows Go to Settings to activate Windows. Current Worksheet: Worksheet 1 Type here to search 0 IT Editable 5:40 AM 7/31/2020 e R *

- Minitab - Untitled Eile Edit Data Calc Stat Graph Editor Tools Window Help Assistant jij门的 BOGORE- %% 2 | +Y2 X Q TO Session Interval Plot of y1, y2, ... X Factor Factor Levels 4 Values yi, y2, y3, y4 Interval Plot of y1, y2, ... 99% CI for the Mean Analysis of Variance F-Value 11.02 38 Source Factor Error Total P-Value 0.000 DF 3 36 39 Seg ss 517.7 563.6 1081.3 Adj ss 517.7 563.6 Contribution 47.88% 52.12% 100.00% Adj MS 172.56 15.66 36 Model Summary 34 S 3.95671 R-sa 47.888 R-sq(adj) 43.53% PRESS 695.802 R-sq (pred) 35.65% 32 Means Factor 30 y1 y2 y3 y4 N 10 10 10 10 Mean 26.12 24.70 30.140 33.90 St Dev 3.33 4.46 3.016 4.75 99% CI (22.72, 29.52) ( 21.30, 28.10) (26.737, 33.543) (30.50, 37.30) Data 28 Pooled StDev = 3.95671 26 Interval Plot of y1, y2, ... 24 Inverse Cumulative Distribution Function 22 F distribution with 3 DF in numerator and 36 DF in denominator P ( XS x) 0.99 4.37710 y3 y4 20 y1 y2 The pooled standard deviation was used to calculate the intervals. Activate Windows Current Worksheet: Worksheet 1 Type here to search מחר e R 5:40 AM 7/31/2020