Question

Afuel economy study was conducted for two German automobiles, Mercedes and Volkswagen. One vehicle of each brand was selected, and the mileage performed was observed for 10 tanks of fuel in each car. Assume that the data are from normal populations. The data are as follows (in miles per gallon): Mercedes: 24.4 25.0 24.8 24.6 24.9 24.6 24.7 24.9 24.5 24.8 Volkswagen: 41.8 43.5 42.3 424 41.6 39.9 39.5 40.8 41.9 39.6 Using a 95% confidence interval, is there evidence to support the claim that the variability in mileage performance is greater for a Volkswagen than for a Mercedes? No. 47.86 <oV20M 2. Round your answer to two decimal places (e.g. 98.76). Statistical Tables and Charts

Answer 1

n 10 9 Q = 5% Sample Std deviation (SM) for Mercedes = 0.19 Sample sto deviation (Sv) for Volkswagen = 1.34 95% Confidence interval for two population variances is: + į Sr Fg, SÅ Fogg 0.192 L. * 4.026 1.342 4.026 1:34 0.0052 20m2 (0.0841 2 sMx 2 2 S} < 0.192 2 2 ora 192-31 > Ove > 11.89 OM

OM² Since, The Confidence interval for en ov is greater than 80 , we support the claim that the variability in mileage performance is greater for a volkswagen than for a mercedes :

2%2% Points for the F distribution v = 1 2 3 4 5 6 7 8 9 10 12 21 V2 2 3 4 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956,6 963.3 9686 976.7 997.3 1018 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39 39 39 40 3941 39 46 39.50 17.44 16.04 15.44 15.10 14.88 1473 14.62 14.54 1447 1442 14.34 14.12. 13.90 12.22 10.65 9.979 9.605 9.364 9.197 9.074 8.980 8.905 8.844 8.751 8.511 3.257 10.01 8.434 7.764 7.388 7.146 6.978 6.853 6.757 6,681 6,619 6,525 6.278 6015 8.813 7.260 6.599 6.227 5.988 5.820 5.695 5.600 5.523 5461 5.366 5.117 4849 8.073 6.542 5.890 5.523 5.285 5.119 4.995 4.899 4.823 4.761 4.666 4415 4.142 7.571 6.059 5.416 5.053 4.817 4.652 4.529 4.433 4,357 4295 4.200 3.947 3.670 7.209 5.715 5.078 4.718 4.484 4.320 4.197 4.102 4.026 3.964 3.868 3.614 3.333 5 6 7 8 9 10 11 12 13 14 6.937 5.456 4.826 4.468 4.236 4.072 3.950 3.855 3.779 3.717 3.621 3.365 3.080 6.724 5.256 4.630 4.275 4.044 3.881 3.759 3.664 3.588 3.526 3430 3.173 2.883 6.554 5.096 4.474 4.121 3.891 3.728 3.607 3.512 3436 3.374 3277 3.019 2.725 6.414 4.965 4.347 3.996 3.767 3.604 3.483 3.388 3.312 3.250 3.153 2.893 2.596 6.298 4.857 4.242 3.892 3.663 3.501 3.380 3.285 3.209 3.147 3.050 2,789 2487 6.200 4.765 4.153 3.804 3.576 3.415 3.293 3.199 3.123 3.060 2.963 2.701 2.395 6.115 4.687 4.077 3.729 3.502 3.341 3.219 3.125 3.049 2.986 2.889 2.625 2.316 6.042 4.619 4.011 3.665 3.438 3.277 3.156 3.061 2.985 2.922 2.825 2.560 2.248 5.978 4.560 3.954 3.608 3.382 3.221 3.100 3.005 2.929 2.866 2.799 2.503 2.187 5.922 4.508 3.903 3.559 3.333 3.172 3.051 2.956 2.880 2.817 2.720 2452 2.133 15 16 17 18 19 20 21 22 23 24 5.871 4.461 3.859 3.515 3.289 3.128 3.007 2.913 2.837 2.774 2.676 2408 2.085 5.827 4.420 3.819 3.475 3.250 3.090 2.969 2.874 2.798 2.735 2.637 2.368 2.042 5.786 4.383 3.783 3.440 3.215 3.055 2.934 2.839 2.763 2.700 2.602 2.332 2003 5.750 4.349 3.750 3.408 3.183 3.023 2.902 2.808 2.731 2.668 2.570 2.299 1.968 5.717 4.319 3.721 3.379 3.155 2.995 2.874 2.779 2.703 2.640 2.541 2.269 1.935 5.686 4.291 3.694 3.353 3.129 2.969 2.848 2.753 2.677 2.613 2.515 2.242 1.906 5.659 4.265 3.670 3.329 3.105 2.945 2.824 2.729 2.653 2.590 2491 2.217 1.878 5.633 4.242 3.647 3.307 3.083 2.923 2.802 2.707 2.631 2.568 2469 2.195 1.853 5.610 4.221 3.626 3.286 3.063 2.903 2.782 2.687 2.611 2.547 2.448 2.174 1.829 5.588 4.201 3.607 3.267 3.044 2.884 2.763 2.669 2.592 2.529 2430 2.154 1.807 25 26 27 28 29 30 32 34 36 38 5.568 4.182 3.589 3.250 3.026 2.867 2.746 2.651 2.575 2.511 2412 2.136 1787 5.531 4.149 3.557 3.218 2.995 2.836 2.715 2.620 2.543 2.480 2.381 2.103 1.750 5.499 4.120 3.529 3.191 2.968 2.808 2.688 2.593 2.516 2453 2.353 2.075 1.717 5.471 4.094 3.505 3.167 2.944 2.785 2.664 2.569 2.492 2.429 2.329 2.049 1.687 5.446 4.071 3.483 3.145 2.923 2.763 2.643 2.548 2.471 2.407 2.307 2.027 1.661 40 60 120 5.424 4.051 3.463 3.126 2.904 2.744 2.624 2.529 2452 2.388 2.288 2.007 1.637 5.286 3.925 3.343 3.008 2.786 2.627 2.507 2.412 2.334 2.270 2.169 1.882 1482 5.152 3.805 3.227 2.894 2.674 2.515 2.395 2.299 2.222 2.157 2055 1.760 1.311 5.024 3.689 3.116 2.786 2.567 2.408 2.288 2.192 2.114 2.048 1.945 1.640 1.000