TABLE D The t distribution* Confidence interval percents (two-tailed) 80% 90% 95% 98% 99% 99.9% a level for two-tailed test 20 .10 .05 .02 .01 .001 a level for one-tailed test df .10 .05 025 01 005 .0005 3.078 6.314 12.71 31.82 63.66 636.6 1.886 2.920 4.303 6.965 9.925 31.598 1.638 2.353 3.182 4.541 5.841 12.924 1.533 2.132 2.776 3.747 4.604 8.610 1.476 2.015 2.571 3.365 4.032 6.869 1.440 1.943 2.447 3.143 3.707 5.959 1.415 1.895 2.365 2.998 3.499 5.408 1.397 1.860 2.306 2.896 3.355 5.041 1.383 1.833 2.262 2.821 3.250 4.781 1.372 1.812 2.228 2.764 3.169 4.587 1.363 1.796 2.201 2.718 3.106 4.437 1.356 1.782 2.179 2.681 3.055 4.318 1.350 1.771 2.160 2.650 3.012 4.221 1.345 1.761 2.145 2.624 2.977 4.140 1.341 1.753 2.131 2.602 2.947 4.073 16 1.337 1.746 2.120 2.583 2.921 4.015 1.333 1.740 2.110 2.567 2.898 3.965 18 1.330 1.734 2.101 2.552 2.878 3.922 1.328 1.729 2.093 2.539 2.861 3.883 1.325 1.725 2.086 2.528 2.845 3.850 1.323 1.721 2.080 2.518 2.831 3.819 1.32 1.717 2.074 2.508 2.819 3.792 1.319 1.714 2.069 2.500 2.807 3.767 1.318 1.711 2.064 2.492 2.797 3.745 1.316 1.708 2.060 2.485 2.787 3.725 1.315 1.706 2.056 2.479 2.779 3.707 1.314 1.703 2.052 2.473 2.771 3.690 1.313 1.701 2.048 2.467 2.763 3.674 1.311 1.699 2.045 2.462 2.756 3.659 1.310 1.697 2.042 2.457 2.750 3.646 1.303 1.684 2.021 2.423 2.704 3.551 1.299 1.676 2.009 2.403 2.678 3.496 1.296 1.671 2.000 2.390 2.660 3.460 80 1.292 1.664 1.990 2.374 2.639 3.416 100 1.290 1.660 1.984 2.364 2.626 3.390 120 1.289 1.658 1.980 2.358 2.617 3.373 oo 1.282 1.645 1.960 2.326 2.576 3.291 * To be significant, the / obtained from the data must be equal to or greater than the value shown in the table. Source: Reprinted by permission of Pearson Education Ltd.TABLE F (continued) Degrees of freedom (for the numerator of F ratio) 50 75 100 200 500 00 1 2 3 4 S 6 7 8 10 11 12 14 16 20 24 30 40 2.31 2.27 2.21 14 4.60 3.74 3.11 2.96 2.85 2.44 2.35 5.56 5.03 15 2.77 16 17 6.11 19 4.35 Degrees of freedom (for the denom 22 2.78 2.70 2.62 2.13 24 2.23 2.27 2.33 2.21 1.77 1.74 1.72 1.71 25 25 2.24 2.20 2.16 2.70 2.27 5.57 2.15 2.10 2.05 26 4.22 3.37 2.98 2.19 2.15 2.13 1.72 3.59 3.42 3.29 3.17 3.09 3.02 2.96 2.86 2.77 14 TABLE G Critical values of the studentized range statistic (for Tukey HSD tests) a = .05 Number of levels of the independent variable 2 5 6 8 10 11 12 13 14 15 dif error 53.20 54.33 55.3 17.97 26.98 32.82 37.07 40.41 43.12 45.40 47.36 49.07 50.59 $1.96 15.08 15.38 15.65 6.08 8.33 9.80 10.88 11.74 12.44 13.03 13.54 13.99 14.3 14.75 8.04 8.48 8.85 9.18 9.46 9.72 9.95 10.15 10.35 10.53 4.50 5.91 6.82 7.50 6.29 6.71 7.05 7.35 7.60 7.33 8.03 8.21 8.37 8.52 8.66 3.93 5.04 5.76 3.64 4.60 5.22 5.67 6.03 6.33 6.58 6.80 7.00 7.17 7.32 7.47 7.60 7.72 10 0 0 V auAWN - 3.46 4.34 4.90 5.31 5.63 5.90 6.12 6.32 6.49 6.65 6.79 6.92 7.03 7.14 3.34 4.16 1.68 5.06 5.36 5.61 5.82 6.00 6.16 6.3 6.43 6.55 6.66 6.76 3.26 4.04 1.53 4.89 5.17 5.40 5.60 5.77 5.92 6.05 6.18 6.29 6.39 6.48 3.20 3.95 4.42 4.76 5.02 5.24 5.43 5.60 5.74 5.87 5.98 6.09 6.19 6.28 10 3.15 3.88 1.33 4.65 4.91 5.12 5.30 5.46 5.60 5.72 5.83 5.94 6.03 6.11 3.82 4.26 4.57 4.82 5.03 5.20 5.35 5.49 5.60 5.71 5.81 5.90 5.98 3.11 3.08 .77 4.20 4.51 4.75 4.95 5.12 5.26 5.40 5.51 5.62 5.71 5.79 5.88 4.15 4.45 4.69 4.88 5.05 5.19 5.32 5.43 5.53 5.63 5.71 5.79 3.0 3.74 4.11 4.41 4.64 4.83 4.99 5.13 5.25 5.36 5.46 5.55 5.64 5.71 3.03 3.70 5.49 5.57 5.65 3.01 3.67 108 4.37 1.60 4.78 194 5.08 5.20 5.31 5.40 5.59 16 3.00 3.65 LOS 4.33 4.56 4.74 4.90 5.03 5.15 5.26 5.35 5.44 5.52 2.98 3.63 4.02 4.30 4.52 4,70 4.86 4.99 5.11 5.21 5.31 5.39 5.47 5.54 2.97 4.00 4.28 4.50 4.67 4.82 4.96 5.07 5.17 5.27 5.35 5.43 5.50 18 3.61 5.23 5.32 5.39 5.46 19 2.96 3.59 3.98 4.25 4.47 4.64 4.79 4.92 5.04 5.14 20 2.95 3.58 3.96 4.23 1.44 4.62 4.77 4.90 5.01 5.11 5.20 5.28 5.36 5.43 5.25 5.32 24 2.92 3.53 3.90 4.17 4.37 1.54 4.68 4.81 4.92 5.01 5.10 5.18 4.92 5.08 5.15 5.21 30 5.00 2.89 3.49 3.84 4.10 4.30 4.46 4.60 4.72 4.82 1.39 4.52 4.64 4.74 4.82 4.90 4.98 5.04 5.11 40 2.86 3.44 3.79 4.04 4.23 4.73 4.81 4.88 4.94 5.00 60 2.83 3.40 3.74 3.98 4.16 4.31 4.44 4.55 4.65 4.84 4.90 120 2.80 3.36 3.69 3.92 4.10 4.24 4.36 4.47 4.56 4.64 4.71 4.78 4.74 1 80 0O 2.77 3.31 3.63 3.86 4.03 4.17 4.29 4.39 4.47 4.55 4.62 4.68 (continued) Source: From "Tables of Range and Studentized Range," by H. L. Harter, 1960, Annals of Mathematical Statistics, 31, 1122-1147. Copyright @ 1960 The Institute of Mathematical Statistics. Reprinted with permission.2. Paired samples t-test: A researcher hypothesized that college students would have a tendency to be more liberal at the end of college relative to the beginning. A researcher measured the political orientation of 12 college freshmen using a scale that ranged from liberal to conservative (1 being extremely liberal; 6 being extremely conservative). Four years later, just before graduation, the same 12 students reported their political orientation again. The following scores were obtained. points) 2008 2012 (X1) (X2) SI 4 N N ANWNAAWARAUN AAWANT WI S12 M Difference = .58 SD Difference = 2.31 a. Determine the independent variable, levels of the independent variable, and the dependent variable. 9 b. State the null as well as the alternative hypothesis. Be sure to include symbols and words. c. Identify the critical value and draw a rejection region. Be sure to note the alpha level (i.e., the criterion) and degrees of freedom associated with this value