Determine if there is a significant difference between the segments of the USA.

Question

Determine if there is a significant difference between the segments of the USA. What is the F value?

Northeast Southeast Northwest Southwest 0.31754 0.549516049 0.803216786 0.353032 0.953352 1.371629229 1.063736764 0.8867677 0.659425 0.728820834 0.904878591 0.4182003 0.009508 1.400711901 0.985696939 0.9895923 0.212277 0.654398833 1.272398413 0.2248771 0.222645 0.608575713 1.195048426 0.2524244 0.470496 0.653158072 1.179347843 0.039735 0.319933 0.836736155 1.277837088 0.8589175 0.469795 1.487388675 0.942754233 0.1148356 0.72048 1.317549025 0.980623762 0.9657925 0.319754 0.71253898 1.185685747 0.3179975 0.521575 1.088787568 1.091153989 0.1461059 0.767463 0.712563162 1.688888871 0.1282949 0.81192 1.248801627 0.720668337 0.2160137 0.947411 1.462246375 1.299514881 0.2062526 0.408297 1.114693266 1.064611553 0.2845799 0.873691 1.081265593 0.864039086 0.4370647 0.09409 1.196756841 1.233360038 0.7581724 0.541705 1.468476253 0.851612225 0.9509338 0.339327 1.155652376 1.511335789 0.3890403 0.12526 1.148290189 0.83379827 0.6431253 0.69975 1.035029644 1.130323017 0.7886785 0.667815 1.255598505 1.016638356 0.5482001 0.635836 1.265456619 1.255067361 0.9766515 0.492795 0.70562621 1.349981913 0.623492 0.768534 0.565692189 0.730684285 0.4038454 0.026473 0.781653612 0.885067757 0.8017614 0.899954 0.744799368 0.741565933 0.9054311 0.292912 0.666745966 1.694798276 0.5020147 0.708195 0.898749549 1.446368864 0.0901391 0.95596 0.926239214 1.404421757 0.9912534 0.518945 1.118741147 0.878540752 0.3019325 0.060899 1.154338058 0.76340824 0.3683206 0.468773 0.815635503 0.737099626 0.0829592 0.776736 1.428323028 1.685018208 0.8210246 0.27264 1.382522215 0.862825228 0.0632315 0.679338 1.373983637 1.114093325 0.5496238 0.484859 0.689596067 1.063722761 0.2554149 0.743589 0.51997336 1.320522222 0.633587 0.585835 1.09994739 1.589111356 0.6555198 0.864937 1.356528903 1.007044111 0.9809152 0.275632 1.49084873 1.295517945 0.7971541 0.213595 1.258932143 0.781631115 0.1963526 0.350145 0.745993268 0.948568541 0.7667747 0.052721 1.402444636 0.715861687 0.3192148 0.425964 0.836548416 1.494594993 0.6847825 0.389778 0.765841829 1.059695134 0.2723647 0.964911 1.132202849 1.404736755 0.679983 0.792287 0.734669773 1.216461925 0.2256663 0.569547 1.107035994 1.380754832 0.9026863 0.184034 0.653942891 1.59440973 0.9221129 0.92778 1.428664217 0.996025135 0.5238443 0.159302 0.888932385 1.670709129 0.1601483 0.555249 0.837175257 1.204842919 0.7823247 0.333585 1.320223131 0.933517576 0.345436 0.994751 1.282612349 1.379619665 0.5088053 0.139884 1.301796927 1.664841526 0.9460396 0.283718 1.390410208 1.181720697 0.6568471 0.779941 0.502230332 1.15996859 0.9415544 0.483972 0.767244549 1.125731368 0.656535 0.652234 0.656670639 1.256351214 0.6981775 0.383264 1.421360386 0.979834626 0.8231933 0.566968 1.12843161 1.140583875 0.4612018 0.785005 1.272225678 1.499791935 0.1272749 0.022053 0.676906399 1.441577547 0.2808053 0.591071 1.276261778 1.048100479 0.9405217 0.413116 0.837711404 0.899727167 0.7077244 0.736226 0.714227751 1.410010709 0.2023413 0.784584 0.513460812 0.945910336 0.9237316 0.924581 1.038015833 0.808435913 0.5326156 0.11292 1.101083659 0.776432131 0.620376 0.646225 0.564305145 1.28493039 0.6883296 0.798093 1.344836634 0.995787072 0.2731095 0.054435 1.126998091 1.616835264 0.9178542 0.543402 0.926253296 1.427665613 0.3661335 0.305436 1.180036527 1.080535107 0.5544909 0.309375 1.004670188 0.788821343 0.348822 0.501854 0.708264966 1.046445754 0.0681674 0.340558 1.148571848 1.456820708 0.6350225 0.998037 1.307717202 1.466040999 0.8911971 0.796052 0.954109629 0.910622211 0.9725593 0.963886 0.953449071 1.199047489 0.7787443 0.991221 0.841987123 1.177704789 0.5346867 0.969543 0.613447546 0.773544067 0.3428925 0.077587 0.540685221 1.606451093 0.6567764 0.945151 1.235950928 1.017394885 0.5874771 0.792178 0.969245077 1.545222856 0.6267938 0.729822 0.620768711 0.746156431 0.8622779 0.15795 1.238603231 1.014149803 0.3653026 0.942843 1.258878853 1.097025332 0.4794082 0.827118 0.588974685 1.236824963 0.4844662 0.265491 1.40428217 1.416828284 0.4941888 0.936428 1.207000555 1.35757372 0.1284342 0.326754 0.980149996 1.342910055 0.2790396 0.115475 0.946619297 1.129361321 0.7823247 0.530444 1.043447777 1.258639885 0.0942772 0.142203 1.360237218 1.228830066 0.7860393 0.722502 1.04034409 1.578154918 0.8862354 0.810963 1.234129294 1.562454755 0.0537196 0.694616 0.878999648 1.372726868 0.3607558 0.450452 0.658210117 1.391548071 0.595462 0.36207 0.905864225 1.634512228 0.0445598 0.941652 1.006111549 1.094003713 0.0679559 0.40788 1.168177209 0.733112481 0.3682718 0.015573 1.276515741 0.840022099 0.0643913 0.674958 0.571190101 1.539700583 0.729509 0.469431 1.139644952 1.216403392 0.0920819 0.916853 0.976709803 1.622665552 0.0617192 0.74814 1.069330294 1.00262397 0.0307327 0.817513 1.452760737 1.233427536 0.3365904 0.014466 1.389915792 1.566876208 0.8950854 0.292241 0.815508435 1.594673633 0.9616803 0.077855 1.463564423 1.453540136 0.238016 0.600082 0.593868245 1.327280126 0.8597371 0.172822 1.093711936 1.364619471 0.2813035 0.745658 1.176443123 1.334219254 0.5389238 0.357645 0.689648533 1.003378496 0.8600968 0.289347 0.566010606 1.455981451 0.56972 0.79369 1.351352694 0.724864696 0.3146612 0.997116 1.250874973 1.380870481 0.1623022 0.575001 1.140828797 1.310210651 0.7184432 0.406258 0.676595889 1.104555569 0.8963379 0.977733 1.188734226 1.638748026 0.654111 0.070063 0.524575316 1.040758601 0.5304369 0.11862 0.945047134 0.800852909 0.8582292 0.772697 0.86890862 1.509503727 0.6705993 0.053306 0.962402256 1.139888502 0.0748409 0.736213 1.449843293 1.395180035 0.4475377 0.324316 0.782189245 1.687904697 0.3043425 0.125268 1.299805265 1.142248103 0.5491227 0.265572 0.926179778 1.082846132 0.1745674

Explanation / Answer

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

F value = 186.39

Option D is correct.

Column n Mean Std. Dev. Std. Error Northeast 131 0.52187534 0.29722072 0.025968295 Southeast 131 1.014285 0.28795023 0.025158328 Northwest 131 1.1919466 0.27657879 0.024164801 Southwest 131 0.51742929 0.2933576 0.025630773

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