We want to find out if college students trust a presidential candidate (in this case Mitt Romney). We randomly select 29 college students from a national registry (assuming there was such a thing) and ask them to rate how trustworthy they find Mitt Romney on a scale of 0 to 7 with 0 being completely untrustworthy and 7 being completely trustworthy. Thesample of 29 studentsresults in anaverage of 3.94 points. Since3.5 is the middle or neutral value, we are going to treat it as the “standard” or the assumed “no effect” value. We will also assume asample standard deviation (sigma) of 2 points.
The null hypothesis in this case is that college students’ average trust rating for Mitt Romney = 3.5 (the neutral value).
a. There are three options for the alternative hypothesis. Choose one and make a statement of your alternative hypothesis.
b. Use the t-test formula for statistical significance to calculate the value of “t.” What does this value tell us (in units of standard error) about Mitt Romney’s average rating compared to the neutral value of 3.5?
c. Using Table C from the text (also pasted below), find the appropriate row based on the degrees of freedom to determine and report the critical value for alpha = .05.
d. Now approximate the p-value for the result you found in part “b”. (Hint: remember to use one-sided or two-sided based on the type of alternative hypothesis you stated. You should be able to say the p-value is between ____ and ____).
e. Assuming an alpha level of .05: Based on the result from C, do we have statistical significance? Can we reject the null? Why?
Extracted text: Table entry for C is the critical value * required for confidence level C. To approximate one- and two-sided Pvalues, compare the value of the t Tail area 15 statistic with the critical values of Area C that match the Pvalues given at the bottom of the table. TABLE C tDISTRIBUTION CRITICAL VALUES CONFIDENCE LEVEL C DEGREES OF FREEDOM 50% 60% 70% 80% 90% 95% 96% 98% 99% 99.5% 99.8% 99.9% 1.000 1.376 1.963 3.078 6.314 12.71 0.816 1.061 1.386 1.886 2.920 0.765 0.978 1.250 1.638 2.353 0.741 0.941 1.190 1.533 2.132 0.727 0.920 1.156 1.476 2.015 15.89 4.849 3.482 2.999 2.757 63.66 9.925 5.841 4.604 4.032 127.3 14.09 7.453 5.598 4.773 318.3 22.33 10.21 7.173 5.893 636.6 31.60 12.92 8.610 6.869 31.82 4.303 3.182 2.776 2.571 6.965 4.541 3.747 3.365 2 000 4 5.959 3.707 3.499 3.355 3.250 3.169 5.208 4.785 4.501 4.297 4.144 4.317 0.718 0.906 1.134 1.440 1.943 0.711 0.896 1.119 1.415 1.895 0.706 0.889 1.108 1.397 1.860 0.703 0.883 1.100 1.383 1.833 0.700 0.879 1.093 1.372 1.812 2.447 2.365 2.306 2.262 2.228 2.612 2.517 2.449 2.398 2.359 3.143 2.998 2.896 2.821 2.764 6. 4.029 3.833 3.690 3.581 5.408 5.041 4.781 4.587 7. 10 0.697 0.876 1.088 1.363 1.796 0.695 0.873 1.083 1.356 1.782 0.694 0.870 1.079 1.350 1.771 0.692 0.868 1.076 1.345 1.761 0.691 0.866 1.074 1.341 1.753 2.201 2.179 2.160 2.145 2.131 2.328 2.303 2.282 2.264 2.249 2.718 2.681 2.650 2.624 2.602 3.106 3.055 3.012 2.977 2.947 3.497 3.428 3.372 3.326 3.286 4.025 3.930 3.852 3.787 3.733 4.437 4.318 4.221 4.140 4.073 11 12 13 14 15 0.690 0.865 1.071 1.337 1.746 0.689 0.863 1.069 1.333 1.740 0.688 0.862 1.067 1.330 1.734 0.688 0.861 1.066 1.328 1.729 0.687 0.860 1.064 1.325 1.725 2.120 2.110 2.101 2.093 2.086 2.235 2.224 2.214 2.205 2.197 2.583 2.567 2.552 2.539 2.528 2.921 2.898 2.878 2.861 2.845 3.252 3.222 3.197 3.174 3.153 3.686 3.646 3.611 3.579 3.552 4.015 3.965 3.922 3.883 3.850 16 17 18 19 20 3.527 3.505 3.485 3.819 21 22 23 24 25 0.686 0.859 1.063 1.323 1.721 0.686 0.858 1.061 1.321 1.717 0.685 0.858 1.060 1.319 1.714 0.685 0.857 1.059 1.318 1.711 0.684 0.856 1.058 1.316 1.708 2.080 2.074 2.069 2.064 2.060 2.189 2.183 2.177 2.172 2.167 2.518 2.508 2.500 2.492 2.485 2.831 2.819 2.807 3.135 3.119 3.104 3.792 3.768 2.797 2.787 3.091 3.078 3.467 3.450 3.745 3.725 3.067 3.057 3.047 3.038 3.030 3.707 26 27 28 29 30 0.684 0.856 1.058 1.315 1.706 2.056 2.052 2.048 2.045 2.042 1.703 0.683 0.855 1.056 1.313 1.701 1.699 1.310 1.697 2.162 2.158 2.154 2.150 2.147 2.479 2.473 2.467 2.462 2.457 2.779 2.771 2.763 2.756 2.750 3.435 3.421 3.408 3.396 3.385 3.690 3.674 3.659 3.646 0.684 0.855 1.057 1.314 0.683 0.854 1.055 1.311 0.683 0.854 1.055 2.423 2.403 2.390 2.374 2.704 2.678 2.660 2.639 2.626 2.581 2.971 2.937 2.915 2.887 2.871 2.813 3.307 3.261 3.232 3.195 3.174 3.098 3.551 3.496 3.460 3.416 3.390 3.300 2.123 2.109 2.099 40 50 60 80 100 1000 0.681 0.851 1.050 1.303 1.684 0.679 0.849 1.047 1.299 1.676 0.679 0.848 1.045 1.296 1.671 0.678 0.846 0.677 0.845 1.042 1.290 1.660 0.675 0.842 1.037 1.282 1.646 2.021 2.009 2.000 1.990 1.984 1.962 2.088 2.081 2.056 1.043 1.292 1.664 2.364 2.330 0.674 0.841 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.091 3.291 One-sided P .25 .20 .15 .10 .05 .025 .02 „01 .005 „0025 .001 .0005 Two-sided P 50 40 30 .20 .10 .05 .04 .02 .01 „005 .002 .001