2 Exercise 10-2 Algo Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the its appropriate table: ztable or [ table) n .-26.0 12 . -25.7 eBook 1 - 8.0 $3 . 8.8 Print 01 = 17 82 - 26 iferences a. Construct the 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal. (Round final answers to 2 decimal places.) Confidence interval is to b. Specify the competing hypotheses in order to determine whether or not the population means differ. O He: #1 - 12 = 0; HA: 1 - H2 # @ OMe: #1 - 12 2 0; HA: W1 - H2 OK nt c. Using the confidence interval from part a, can you reject the null hypothesis? Inces Yes, since the confidence interval includes the hypothesized value of 0. Yes, since the confidence interval does not include the hypothesized value of 0. O No, since the confidence interval includes the hypothesized value of 0. O No, since the confidence interval does not include the hypothesized value of 0. d. Interpret the results at a = 0.05. O We cannot conclude that population mean 1 is greater than population mean 2. O We conclude that population mean 1 is greater than population mean 2. O We cannot conclude that the population means differ. We conclude that the population means differ.TABLE 2 Student's t Distribution Entries in this table provide the values of fay 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, P(710 2 1.812) = 0.05. Area in Upper Tail, a df 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 2.776 3.747 4.604 0.920 1.476 2.015 2.571 3.365 4.032 0.906 1.440 1.943 2.447 3.143 3.707 0.896 1.415 1.895 2.365 2.998 3.499 00 0.889 1.397 1.860 2.306 2.896 3.355 0.883 1.383 1.833 2.262 2.821 3.250 10 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 12 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 20 0.860 1.325 1.725 2.086 2.528 2.845 21 0.859 1.323 1.721 2.080 2.518 2.831 22 0.858 1.321 1.717 2.074 2.508 2.819 23 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 2.771 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 2.024 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 2.018 2.418 2.698 43 0.850 1.302 1.681 2.017 2.416 2.695 44 0.850 1.301 1.680 2.015 2.414 2.692 45 0.850 1.301 1.679 2.014 2.412 2.690 46 0.850 1.300 1.679 2.013 2.410 2.687 47 0.849 1.300 1.678 2.012 2.408 2.685 48 0.849 1.299 1.677 2.011 2.407 2.682 49 0.849 1.299 1.677 2.010 2.405 2.680 50 0.849 1.299 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 2.002 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 80 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 Source: I values calculated with Excel