For problems involving Analysis of Variance you must 1 stat

. For problems involving Analysis of Variance, you must (1) state the type of ANOVA, (2) state the dependent variable, (3) distinguish each causal variable (factor) as fixed or random, (4) present your results in an ANOVA table, (5) explicitly state each null hypothesis that you are testing, and (6) state whether you accept or reject these null hypotheses, (7) include a sentence or two of interpretation.

Mold spores are an important allergen throughout the United States. The spores are produced by fungi that typically grow in damp areas of houses, frequently in the basement. The toxicity of spores can be measured as a continuous variable. A mycologist is interested in whether toxicity varies among houses and whether there is variability between fungal colonies within a house. He randomly selects 12 houses within Lawrence, Kansas. From each house, he collects 3-5 colonies. Each colony is then cultured in the lab and 4 measurements of toxicity are taken for each colony. Perform an appropriate statistical analysis to address the following questions:

(1) What fraction of the total variance in toxicity exists among houses?

(2) What fraction of the total variance in toxicity exists among colonies within houses?

(3) What fraction of the total variance in toxicity is due to other causes?

House
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colony
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sample
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toxicity
9.298
8.8321
10.151
11.9695
12.5622
13.1564
12.8354
12.7085
13.8574
13.6735
13.9577
14.014
19.6143
12.1099
11.1607
14.3877
9.6303
11.5251
13.5257
13.2456
11.5212
16.6228
13.449
12.8039
8.9916
14.0592
11.734
18.3754
16.6488
12.7427
15.247
13.7793
15.4971
10.9496
15.395
15.4436
13.6633
8.5723
11.5221
13.753
12.3472
11.8054
12.7951
10.2802
14.6209
9.3425
17.6556
14.0799
11.1747
14.0067
10.0835
13.7145
12.7371
8.7069
12.9197
10.2389
13.2238
15.1896
14.0563
13.9206
15.2879
14.7543
17.5757
16.4506
12.8807
15.8013
13.3892
15.4365
13.5821
10.0251
8.6979
11.7054
8.6632
14.8384
10.4613
11.172
11.0196
15.6936
11.4945
12.4015
11.8484
12.7177
13.7413
16.9046
14.727
16.5471
15.6806
13.398
14.0476
13.5422
10.2526
11.5225
11.0306
14.2919
15.3419
15.0655
10.0176
11.8189
9.53
13.3368
13.3577
12.4494
12.2015
13.8225
11.8399
12.8012
19.0153
11.4946
18.0754
8.6662
10.1189
7.8228
7.5518
11.5254
8.6214
6.7189
4.1149
6.7526
5.0211
6.251
3.5414
7.9716
4.5155
6.3223
7.3432
8.1353
5.8623
4.4216
7.916
7.7745
7.2963
8.4648
10.1527
9.4531
5.973
8.1629
5.9986
6.7521
5.0924
4.2639
4.5311
6.4798
4.6597
5.3074
8.6838
0.2127
3.5381
7.5896
3.3183
8.2087
6.2731
7.7664
10.5198
8.8524
5.4754
9.3287
8.6138
8.0518
6.7825
3.8927
4.9189
5.1434
6.4783
7.3827
4.325
3.3353
3.5781
6.2514
5.5349
8.1731
8.0694
6.2324
7.8887
9.121
5.855
7.1001
7.6603
7.842
9.5557
6.2851
4.0366
7.4916
7.1382
3.9934
6.2179
6.5281
10.0345
11.0995
10.5485
9.2001
10.1601
11.9453
11.7117
7.1942
6.4935
2.9066
8.2559
9.7269
5.5186
7.7939
7.8775
6.4918
4.8564
5.3798
9.6104
4.5269
13.0787
12.5245
10.1599
5.841
3.6059
8.1057
7.8589
7.8185
9.7366
5.5255
9.0103
6.8941

(a) One-way analysis of variance

(b) The house are dependent

random factor is toxicity

(d)

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Row 1 4 12.298 3.0745 17.2142 Row 2 4 12.8321 3.208025 14.2801 Row 3 4 15.151 3.78775 18.88487 Row 4 4 17.9695 4.492375 26.84773 Row 5 4 16.5622 4.14055 31.74408 Row 6 4 18.1564 4.5391 33.22572 Row 7 4 18.8354 4.70885 30.01814 Row 8 4 19.7085 4.927125 28.46658 Row 9 4 18.8574 4.71435 38.04238 Row 10 4 19.6735 4.918375 34.73432 Row 11 4 20.9577 5.239425 34.67036 Row 12 4 22.014 5.5035 33.74605 Row 13 4 25.6143 6.403575 79.56589 Row 14 4 19.1099 4.777475 25.45087 Row 15 4 19.1607 4.790175 19.59271 Row 16 4 23.3877 5.846925 34.41993 Row 17 4 13.6303 3.407575 17.43214 Row 18 4 16.5251 4.131275 24.5194 Row 19 4 19.5257 4.881425 33.87711 Row 20 4 20.2456 5.0614 31.32495 Row 21 4 16.5212 4.1303 24.50018 Row 22 4 22.6228 5.6557 53.45657 Row 23 4 20.449 5.11225 31.11173 Row 24 4 20.8039 5.200975 26.57976 Row 25 4 14.9916 3.7479 12.88728 Row 26 4 21.0592 5.2648 34.59621 Row 27 4 19.734 4.9335 20.77636 Row 28 4 27.3754 6.84385 59.7674 Row 29 4 23.6488 5.9122 52.7887 Row 30 4 20.7427 5.185675 26.2705 Row 31 4 24.247 6.06175 38.16392 Row 32 4 23.7793 5.944825 28.16844 Row 33 4 23.4971 5.874275 44.04389 Row 34 4 19.9496 4.9874 17.79904 Row 35 4 25.395 6.34875 37.92651 Row 36 4 26.4436 6.6109 36.2296 Row 37 4 18.6633 4.665825 36.86869 Row 38 4 14.5723 3.643075 11.46545 Row 39 4 18.5221 4.630525 21.99725 Row 40 4 21.753 5.43825 32.28225 Row 41 4 18.3472 4.5868 27.4328 Row 42 4 18.8054 4.70135 22.65223 Row 43 4 20.7951 5.198775 25.86851 Row 44 4 19.2802 4.82005 13.91699 Row 45 4 21.6209 5.405225 38.63496 Row 46 4 17.3425 4.335625 11.36391 Row 47 4 26.6556 6.6639 53.69665 Row 48 4 24.0799 6.019975 29.0944 Row 49 4 19.1747 4.793675 19.65221 Row 50 4 20.0067 5.001675 38.04021 Row 51 4 17.0835 4.270875 16.57183 Row 52 4 21.7145 5.428625 32.06921 Row 53 4 21.7371 5.434275 25.70278 Row 54 4 15.7069 3.926725 11.71114 Row 55 4 20.9197 5.229925 27.17006 Row 56 4 19.2389 4.809725 13.76708 Row 57 4 23.2238 5.80595 25.34422 Row 58 4 23.1896 5.7974 40.76152 Row 59 4 23.0563 5.764075 31.22711 Row 60 4 23.9206 5.98015 28.24478 Row 61 4 26.2879 6.571975 33.98549 Row 62 4 23.7543 5.938575 36.54089 Row 63 4 27.5757 6.893925 51.60014 Row 64 4 27.4506 6.86265 41.07946 Row 65 4 24.8807 6.220175 19.71671 Row 66 4 25.8013 6.450325 41.75144 Row 67 4 24.3892 6.0973 25.18747 Row 68 4 27.4365 6.859125 33.36505 Row 69 4 26.5821 6.645525 21.60714 Row 70 4 17.0251 4.256275 18.34637 Row 71 4 16.6979 4.174475 11.98283 Row 72 4 20.7054 5.17635 21.61266 Row 73 4 18.6632 4.6658 9.990759 Row 74 4 22.8384 5.7096 39.92666 Row 75 4 19.4613 4.865325 15.91775 Row 76 4 21.172 5.293 16.91673 Row 77 4 22.0196 5.5049 15.07196 Row 78 4 24.6936 6.1734 42.94854 Row 79 4 21.4945 5.373625 18.20672 Row 80 4 23.4015 5.850375 19.96322 Row 81 4 23.8484 5.9621 16.06601 Row 82 4 22.7177 5.679425 24.90547 Row 83 4 24.7413 6.185325 26.93011 Row 84 4 28.9046 7.22615 42.29884 Row 85 4 27.727 6.93175 27.2293 Row 86 4 27.5471 6.886775 45.03195 Row 87 4 27.6806 6.92015 36.1091 Row 88 4 26.398 6.5995 21.43093 Row 89 4 28.0476 7.0119 22.2227 Row 90 4 21.5422 5.38555 35.12486 Row 91 4 19.2526 4.81315 17.81672 Row 92 4 21.5225 5.380625 20.98783 Row 93 4 22.0306 5.50765 17.7791 Row 94 4 23.2919 5.822975 36.54342 Row 95 4 25.3419 6.335475 39.60697 Row 96 4 26.0655 6.516375 35.37224 Row 97 4 22.0176 5.5044 11.71954 Row 98 4 21.8189 5.454725 22.22343 Row 99 4 20.53 5.1325 11.48356 Row 100 4 25.3368 6.3342 23.79396 Row 101 4 26.3577 6.589425 21.91535 Row 102 4 23.4494 5.86235 23.50632 Row 103 4 24.2015 6.050375 19.48282 Row 104 4 26.8225 6.705625 24.06663 Row 105 4 25.8399 6.459975 13.75271 Row 106 4 24.8012 6.2003 24.03195 Row 107 4 32.0153 8.003825 56.77893 Row 108 4 25.4946 6.37365 13.21072 Row 109 4 33.0754 8.26885 43.40819 Row 110 4 17.6662 4.41655 16.02646 Row 111 4 20.1189 5.029725 18.39987 Row 112 4 18.8228 4.7057 10.54058 Row 113 4 19.5518 4.88795 9.153821 Row 114 4 21.5254 5.38135 23.66638 Row 115 4 19.6214 4.90535 11.6929 Row 116 4 18.7189 4.679725 6.514771 Row 117 4 17.1149 4.278725 4.234151 Row 118 4 17.7526 4.43815 8.602968 Row 119 4 17.0211 4.255275 4.927328 Row 120 4 19.251 4.81275 4.474917 Row 121 4 17.5414 4.38535 3.205445 Row 122 4 19.9716 4.9929 9.943402 Row 123 4 17.5155 4.378875 4.230518 Row 124 4 20.3223 5.080575 3.574169 Row 125 4 22.3432 5.5858 3.372647 Row 126 4 21.1353 5.283825 9.83596 Row 127 4 19.8623 4.965575 4.579607 Row 128 4 19.4216 4.8554 2.750303 Row 129 4 23.916 5.979 3.223097 Row 130 4 17.7745 4.443625 15.81988 Row 131 4 18.2963 4.574075 12.84912 Row 132 4 20.4648 5.1162 13.65028 Row 133 4 23.1527 5.788175 16.68848 Row 134 4 20.4531 5.113275 17.92626 Row 135 4 17.973 4.49325 8.973182 Row 136 4 21.1629 5.290725 10.55528 Row 137 4 19.9986 4.99965 6.665734 Row 138 4 18.7521 4.688025 10.56018 Row 139 4 18.0924 4.5231 7.032934 Row 140 4 18.2639 4.565975 5.596111 Row 141 4 19.5311 4.882775 4.721633 Row 142 4 19.4798 4.86995 9.374052 Row 143 4 18.6597 4.664925 6.222234 Row 144 4 20.3074 5.07685 4.69029 Row 145 4 24.6838 6.17095 6.361962 Row 146 4 14.2127 3.553175 13.18168 Row 147 4 18.5381 4.634525 6.534288 Row 148 4 23.5896 5.8974 5.494907 Row 149 4 20.3183 5.079575 4.267595 Row 150 4 19.2087 4.802175 19.37974 Row 151 4 18.2731 4.568275 13.95841 Row 152 4 20.7664 5.1916 14.50204 Row 153 4 24.5198 6.12995 19.45368 Row 154 4 20.8524 5.2131 18.55311 Row 155 4 18.4754 4.61885 11.21497 Row 156 4 23.3287 5.832175 14.98919 Row 157 4 23.6138 5.90345 11.93155 Row 158 4 21.0518 5.26295 15.0123 Row 159 4 20.7825 5.195625 10.67474 Row 160 4 18.8927 4.723175 8.306528 Row 161 4 20.9189 5.229725 6.931828 Row 162 4 19.1434 4.78585 10.94571 Row 163 4 21.4783 5.369575 9.213009 Row 164 4 23.3827 5.845675 7.938865 Row 165 4 21.325 5.33125 6.005573 Row 166 4 18.3353 4.583825 11.35947 Row 167 4 19.5781 4.894525 8.992433 Row 168 4 23.2514 5.81285 6.3077 Row 169 4 23.5349 5.883725 4.720746 Row 170 4 20.1731 5.043275 22.35369 Row 171 4 21.0694 5.26735 19.71177 Row 172 4 20.2324 5.0581 15.50177 Row 173 4 22.8887 5.722175 16.08615 Row 174 4 22.121 5.53025 21.95266 Row 175 4 19.855 4.96375 14.57526 Row 176 4 22.1001 5.525025 13.76927 Row 177 4 23.6603 5.915075 12.90925 Row 178 4 21.842 5.4605 17.40957 Row 179 4 24.5557 6.138925 17.85527 Row 180 4 22.2851 5.571275 11.11535 Row 181 4 21.0366 5.25915 10.21983 Row 182 4 22.4916 5.6229 15.55202 Row 183 4 23.1382 5.78455 12.36994 Row 184 4 20.9934 5.24835 10.25551 Row 185 4 24.2179 6.054475 8.01187 Row 186 4 22.5281 5.632025 13.91242 Row 187 4 23.0345 5.758625 30.34805 Row 188 4 25.0995 6.274875 30.56756 Row 189 4 25.5485 6.387125 26.36313 Row 190 4 25.2001 6.300025 21.29353 Row 191 4 24.1601 6.040025 27.76667 Row 192 4 26.9453 6.736325 30.0593 Row 193 4 27.7117 6.927925 26.39311 Row 194 4 24.1942 6.04855 15.47223 Row 195 4 21.4935 5.373375 19.2243 Row 196 4 18.9066 4.72665 17.69448 Row 197 4 25.2559 6.313975 15.89825 Row 198 4 27.7269 6.931725 16.13911 Row 199 4 21.5186 5.37965 17.56414 Row 200 4 24.7939 6.198475 16.02017 Row 201 4 25.8775 6.469375 13.54792 Row 202 4 25.4918 6.37295 10.89517 Row 203 4 21.8564 5.4641 17.05302 Row 204 4 23.3798 5.84495 14.09616 Row 205 4 28.6104 7.1526 14.24035 Row 206 4 24.5269 6.131725 10.70021 Row 207 4 27.0787 6.769675 44.57947 Row 208 4 27.5245 6.881125 38.82119 Row 209 4 26.1599 6.539975 28.71283 Row 210 4 22.841 5.71025 21.56315 Row 211 4 18.6059 4.651475 25.15255 Row 212 4 24.1057 6.026425 24.14373 Row 213 4 24.8589 6.214725 21.42369 Row 214 4 25.8185 6.454625 19.4934 Row 215 4 25.7366 6.43415 27.73608 Row 216 4 22.5255 5.631375 20.2272 Row 217 4 27.0103 6.752575 20.26548 Row 218 4 25.8941 6.473525 16.30084 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 655.7451 217 3.021867 0.142189 1 1.194482 Within Groups 13899.1 654 21.25244 Total 14554.84 871

. For problems involving Analysis of Variance, you must (1) state the type of ANOVA, (2) state the dependent variable, (3) distinguish each causal variable (fac

For problems involving Analysis of Variance you must 1 stat

Solution

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