Answer Happy

A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 8 of each brand, assigned at random to the left and right rear wheels of 8 taxis. The tires are run until they wear out and the distances, in kilometers, are recorded in the accompanying data set. Find a 99% confidence interval for μ₁ −μ₂. Assume that the differences of the distances are approximately normally distributed. Click here to view the data set Click here to view page 1 of the table of critical values of the t-distribution. Click here to view page 2 of the table of critical values of the t-distribution. Let μ, be the population mean for brand A and let μ₂ be the population mean for brand B. The confidence interval is <H₁-H₂<| (Round to one decimal place as needed.) →
Data Set Taxi 1 2345 6 7 8 Brand A 36,800 35,400 40,500 47,500 43,600 42,500 43,700 34,900 Brand B 37,800 37,100 41,400 46,300 43,000 46,300 45,400 35,600
Critical Values of the t-Distribution (Page 1) 0 Critical Values of the t-Distribution 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 22 23 24 25 0.40 0.325 0.289 0.277 0.271 0.267 26 27 28 29 30 0.265 0.263 0.262 0.261 0.260 0.258 0.257 0.257 19 0.257 20 0.257 0.260 0.259 0.259 0.258 0.258 0.30 0.20 0.727 1.376 0.617 1.061 0.584 0.978 0.569 0.941 0.559 0.920 0.553 0.906 0.896 40 0.255 60 120 0.549 0.546 0.543 0.542 0.540 0.539 0.538 0.537 0.536 0.535 0.534 0.534 0.533 0.533 0.256 0.531 0.256 0.531 0.256 0.530 0.256 0.530 0.256 0.530 0.889 0.883 0.879 0.257 0.532 0.859 0.256 0.532 0.858 0.256 0.532 0.858 0.256 0.531 0.256 0.531 0.876 0.873 0.870 0.868 0.866 0.254 0.527 0.254 0.526 0.253 0.524 0.40 0.30 0.865 0.863 0.862 0.861 0.860 0.15 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.063 1.061 1.060 1.071 1.337 1.069 1.333 1.067 1.330 1.328 0.857 1.059 0.856 1.058 1.066 1.064 1.325 0.856 1.058 0.855 1.057 0.855 1.056 0.854 1.055 0.854 1.055 0.529 0.851 1.050 0.848 1.045 0.845 1.041 0.842 1.036 0.20 0.15 0.10 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 a 1.363 1.356 1.350 1.345 1.341 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.296 1.289 1.282 0.10 0.05 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.671 1.658 1.645 0.05 0.025 12.706 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.000 1.980 1.960 0.025
Critical Values of the t-Distribution (Page 2) Critical Values of the t-Distribution V 1 012 2010 3 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 22 23 24 25 26 27 28 29 30 40 60 120 0.02 15.894 4.849 3.482 V 2.999 2.757 2.612 2.517 19 2.205 20 2.197 2.449 2.398 2.359 2.328 2.303 2.282 2.264 2.249 2.235 2.224 2.214 2.189 2.183 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 2.123 2.099 2.076 2.054 0.02 0.015 21.205 5.643 3.896 3.298 3.003 2.829 2.715 2.634 2.574 2.527 2.491 2.461 2.436 2.415 2.397 2.382 2.368 2.356 2.346 2.336 2.328 2.320 2.313 2.307 2.301 2.296 2.291 2.286 2.282 2.278 2.250 2.223 2.196 2.170 0.015 0.01 31.821 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.358 2.326 0.01 a 0.0075 42.433 8.073 5.047 3.634 3.372 3.203 3.085 2.998 2.932 2.879 2.836 2.801 2.771 2.746 2.724 2.706 2.689 2.674 2.661 2.649 2.639 2.629 2.620 2.612 2.605 2.598 2.592 2.586 2.581 2.542 2.504 2.468 2.432 0.0075 a 0.005 63.656 9.925 5.841 4.604 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2.977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.704 2.660 2.617 2.576 0.005 0.0025 127.321 14.089 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3.286 3.252 3,222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030 2.971 2.915 2.860 2.807 0.0025 0.0005 636.578 31.600 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4.318 4.221 4.140 4.073 4.015 3.965 3.922 3.883 3.850 3.819 3.792 3.768 3.745 3.725 3.707 3.689 3.674 3.660 3.646 3.551 3.460 3.373 3.290 0.0005 I