David Anderson has been working as a lecturer at Michigan State University for the last three years. He teaches two large sections of introductory accounting every semester. While he uses the same lecture notes in both sections, his students in the first section outperform those in the second section. He believes that students in the first section not only tend to get higher scores, they also tend to have lower variability in scores. David decides to carry out a formal test to validate his hunch regarding the difference in average scores. In a random sample of 18 students in the first section, he computes a mean and a standard deviation of 77.4 and 10.8, respectively. In the second section, a random sample of 14 students results in a mean of 74.1 and a standard deviation of 12.2. Sample 1 consists of students in the first section and Sample 2 represents students in the second section. (You may find it useful to reference the appropriate table: z table or t table) a. Construct the null and the alternative hypotheses to test David's hunch. O HO: M1 - H2 = 0; HA: H1 - 12 # 0 O Ho: 11 - H2 20; HA: M1 - 12 0 b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statisticTABLE 2 Student's f Distribution Entries In this table provide the values of try that correspond to a given upper-tail area a and a specified number of degrees of freedom df. For example, for a = 0.05 and of = 10, PUT , 2 1.812) = 0.05. Area In Upper Tall, a 0 0.20 0.10 0.05 0.025 0.01 0,005 1.376 3.078 6.314 12.706 31.821 63.657 1.061 1.886 2.920 4.303 6.965 9.925 0.978 1.638 2.353 3.182 4.541 5.841 0.941 1.533 2.132 2776 3.747 4.604 0.920 1.476 2.015 2571 3.365 4.032 0.906 1.440 1.943 2447 3.143 3.707 0.896 1.415 1.895 2.365 2.998 3.499 0.889 1.397 1.860 2.306 2.896 3.355 0.883 1.383 1.833 2.262 2.821 3.250 0.879 1.372 1.812 2.228 2.764 3.169 11 0.876 1.363 1.796 2.201 2.718 3.106 0.873 1.356 1.782 2.179 2.681 3.055 13 0.870 1.350 1.771 2.160 2.650 3.012 14 0.868 1.345 1.761 2.145 2.624 2.977 15 0.866 1.341 1.753 2.131 2.602 2.947 16 0.865 1.337 1.746 2.120 2.583 2.921 17 0.863 1.333 1.740 2.110 2.567 2.898 18 0.862 1.330 1.734 2.101 2.552 2.878 19 0.861 1.328 1.729 2.093 2.539 2.861 0.860 1.325 1.725 2.086 2.528 2.845 0.859 1.323 1.721 2.080 2.518 2.831 INNY 0.858 1.321 1.717 2.074 2.508 2.819 0.858 1.319 1.714 2.069 2.500 2.807 24 0.857 1.318 1.711 2.064 2.492 2.797 25 0.856 1.316 1.708 2.060 2.485 2.787 26 0.856 1.315 1.706 2.056 2.479 2.779 27 0.855 1.314 1.703 2.052 2.473 2771 28 0.855 1.313 1.701 2.048 2.467 2.763 29 0.854 1.311 1.699 2.045 2.462 2.756 30 0.854 1.310 1.697 2.042 2.457 2.750 31 0.853 1.309 1.696 2.040 2.453 2.744 32 0.853 1.309 1.694 2.037 2.449 2.738 33 0.853 1.308 1.692 2.035 2.445 2.733 34 0.852 1.307 1.691 2.032 2.441 2.728 35 0.852 1.306 1.690 2.030 2.438 2.724 36 0.852 1.306 1.688 2.028 2.434 2.719 37 0.851 1.305 1.687 2.026 2.431 2.715 38 0.851 1.304 1.686 2024 2.429 2.712 39 0.851 1.304 1.685 2.023 2.426 2.708 40 0.851 1.303 1.684 2.021 2.423 2.704 41 0.850 1.303 1.683 2.020 2.421 2.701 42 0.850 1.302 1.682 2018 2.418 2.698 43 0.850 1.302 1.681 2017 2.416 2.695 44 0.850 1.301 1.680 2015 2.414 2.692 45 0.850 1.301 1.679 2.014 2.412 2.690 46 0.850 1.300 1.679 2013 2.410 2.687 47 0.849 1.300 1.678 2.012 2.408 2.685 48 0.849 1.299 1.677 2011 2.407 2.682 49 0.849 1.299 1.677 2.010 2.405 2.680 50 0.849 1.290 1.676 2 009 2.403 2.678 51 0.849 1.298 1.675 2.008 2.402 2.676 52 0.849 1.298 1.675 2.007 2.400 2.674 53 0.848 1.298 1.674 2.006 2.399 2.672 54 0.848 1.297 1.674 2.005 2.397 2.670 55 0.848 1.297 1.673 2.004 2.396 2.668 56 0.848 1.297 1.673 2.003 2.395 2.667 57 0.848 1.297 1.672 2.002 2.394 2.665 58 0.848 1.296 1.672 2002 2.392 2.663 59 0.848 1.296 1.671 2.001 2.391 2.662 60 0.848 1.296 1.671 2.000 2.390 2.660 0.846 1.292 1.664 1.990 2.374 2.639 100 0.845 1.290 1.660 1.984 2.364 2.626 150 0.844 1.287 1.655 1.976 2.351 2.609 200 0.843 1.286 1.653 1.972 2.345 2.601 500 0.842 1.283 1.648 1.965 2.334 2.586 1000 0.842 1.282 1.646 1.962 2.330 2.581 0.842 1.282 1.645 1.960 2.326 2.576