7.2.5 In a study of the nutritional requirements of cattle, researchers measured the weight gains of cows during a 78-day period. For two breeds of cows, Hereford (HH) and Brown Swiss/Hereford (SH), the results are summa- rized in the following table.6 HH SH n 33 51 y 18.3 13.9 S 17.8 19.1 (a) What is the value of the t test statistic for comparing the means? (b) In the context of this study, state the null and alternative hypotheses. (c) The P-value for the t test is 0.29. If a = 0.10, what is your conclusion regarding the hypotheses in (b)? TABLE 4 Critical Values of Student's & Distribution 0 UPPER TAIL PROBABILITY df 0.20 0.10 0.05 0.04 0.03 0.025 0.02 0.01 0.005 0.0005 1 1376 3.078 6.314 7.916 10.579 12.706 15.895 31.821 63.657 636.619 2 1.061 1.886 2.920 3.320 3.896 4.303 4.849 6.965 9.925 31.599 0.978 1.638 2.353 2.605 2.951 3.182 3,482 4.541 5.841 12.924 4 0.941 1.533 2.132 2.333 2.601 2.776 2.999 3.747 4,604 8.610 5 0.920 1.476 2015 2.191 2.422 2.571 2.757 3.365 4.032 6.869 6 0.906 1.440 1.943 2.104 2.313 2.447 2.612 3.143 3.707 5.959 0.896 1.415 1.895 2.046 2.241 2.365 2.517 2.998 3.499 5.408 8 0.889 1397 1.860 2.004 2.189 2.306 2.449 2.896 3.355 5.041 9 0.883 1.383 1.833 1.973 2.150 2.262 2.398 2.821 3.250 4.781 10 0.879 1.372 1.812 1.948 2.120 2.228 2.359 2.764 3.169 4.587 11 0.876 1.363 1.796 1.928 2.096 2.201 2.328 2.718 3.106 4.437 12 0.873 1.356 1.782 1.912 2.076 2.179 2.303 2.681 3.055 4.318 13 0.870 1.350 1.771 1.899 2.060 2.160 2.282 2.650 3.012 4.221 14 0.868 1.345 1.761 1.888 2.046 2.145 2.264 2.624 2.977 4.140 15 0.866 1.341 1.753 1878 2.034 2.131 2.249 2.602 2.947 4.073 16 0.865 1.337 1.746 1.869 2.024 2.120 2.235 2.583 2.921 4.015 17 0.863 1.333 1.740 1.862 2.015 2.110 2.224 2.567 2.898 3.965 18 0.862 1.330 1.734 1.855 2.007 2.101 2.214 2.552 2.878 3.922 19 0.861 1.328 1.729 1.850 2.000 2.093 2.205 2.539 2.861 3.883 20 0.860 1.325 1.725 1.844 1.994 2.086 2.197 2.528 2.845 3.850 21 0.859 1.323 1.721 1.840 1.988 2.080 2.189 2.518 2.831 3.819 0.858 1.321 1.717 1.835 1.983 2.074 2.183 2.508 2.819 3.792 0.858 1.319 1.714 1.832 1.978 2.069 2.177 2.500 2.807 3.768 0.857 1.318 1.711 1.828 1.974 2.064 2.172 2.492 2.797 3.745 0.856 1.316 1.708 1.825 1.970 2.060 2.167 2.485 2.787 3.725 0.856 1.315 1.706 1.822 1.967 2.056 2.162 2.479 2.779 3.707 0.855 1.314 1.703 1.819 1.963 2.052 2.158 2.473 2.771 3.690 0.855 1.313 1.701 1.817 1.960 2.048 2.154 2.467 2.763 3.674 0.854 1.311 1.699 1,814 1.957 2.045 2.150 2.462 2.756 3.659 30 0.854 1.310 1.697 1.812 1.955 2.042 2.147 2.457 2.750 3.646 40 0.851 1.303 1.684 1.796 1.936 2.021 2.123 2.423 2.704 3.551 50 0.849 1.299 1.676 1.787 1.924 2009 2.109 2.403 2.678 3.496 60 0.848 1.296 1.671 1.781 1.917 2.000 2.099 2.390 2.660 3.460 70 0.847 1.294 1.667 1.776 1.912 1.994 2.093 2.381 2.648 3.435 80 0.846 1.292 1.664 1.773 1.908 1.990 2.088 2.374 2.639 3.416 100 0.845 1.290 1.660 1.769 1.902 1.984 2.081 2.364 2.626 3.390 140 0.844 1.288 1.656 1.763 1.896 1.977 2.073 2.353 2.611 3.361 1000 0.842 1.282 1.646 1.752 1.883 1.962 2.056 2.330 2.581 3.300 0.842 1.282 1.645 1.751 1.881 1.960 2.054 2.326 2.576 3.291 60% 80% 90% 92% 94% 95% 96% 98% 99% 99.9% CRITICAL VALUE FOR CONFIDENCE LEVEL