Question

Alejandra is using a one-sample t-test to test the null hypothesis Ho: u = 10.0 against the alternative H1: 4 < 10.0 using a simple random sample of size n = 10. She requires her results to be statistically significant at level a = 0.10. Determine the maximum value of t that will reject this null hypothesis. You may find this table of t-critical values useful. If you are using software, you may find this catalog of software guides useful. Give your answer to three decimal places. t =

Answer 1

solution given He: u=10 H, :u<10 x=0.10 n = 10 The test statistic is t- Z-M slon thil Table value of t at d = 0.10 and n-1=9 di is 1.383. (for one a tailed test. Critical value of t 1.383

t.50 t.80 t95 t 975 t 99 t 999 .9995 cum. prob one-tail two-tails 0.50 1.00 5.75 0.25 0.50 0.20 0.40 0.15 0.30 t 90 0.10 0.20 0.05 0.10 0.025 0.05 0.01 0.02 t 995 0.005 0.001 0.0005 0.01 0.002 0.001 df 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16) 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 601 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 % 1.000 0.816 0.765 0.741 0.727 0.718 0.711 0.706 0.703 0.700 0.697 0.695 0.694 0.692 0.691 0.690 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.685 0.684 0.684 0.684 0.683 0.683 0.683 0.681 0.679 0.678 0.677 0.675 0.674 50% 1.376 1.061 0.978 0.941 0.920 0.906 0.896 0.889 0.883 0.879 0.876 0.873 0.870 0.868 0.866 0.865 0.863 0.862 0.861 0.860 0.859 0.858 0.858 0.857 0.856 0.856 0.855 0.855 0.854 0.854 0.851 0.848 0.846 0.845 0.842 0.842 60% 1.963 1.386 1.250 1.190 1.156 1.134 1.119 1.108 1.100 1.093 1.088 1.083 1.079 1.076 1.074 1.071 1.069 1.067 1.066 1.064 1.063 1.061 1.060 1.059 1.058 1.058 1.057 1.056 1.055 1.055 1.050 1.045 1.043 1.042 1.037 1.036 70% 3.078 6.314 12.71 1.886 2.920 4.303 1.638 2.353 3.182 1.533 2.132 2.776 1.476 2.015 2.571 1.440 1.943 2.447 1.415 1.895 2.365 1.397 1.860 2.306 1.383 1.833 2.262 1.372 1.812 2.228 1.363 1.796 2.201 1.356 1.782 2.179 1.350 1.771 2.160 1.345 1.761 2.145 1.341 1.753 2.131 1.337 1.746 2.120 1.333 1.740 2.110 1.330 1.734 2.101 1.328 1.729 2.093 1.325 1.725 2.086 1.323 1.721 2.080 1.321 1.717 2.074 1.319 1.714 2.069 1.318 1.711 2.064 1.316 1.708 2.060 1.315 1.706 2.056 1.314 1.703 2.052 1.313 1.701 2.048 1.311 1.699 2.045 1.310 1.697 2.042 1.303 1.684 2.021 1.296 1.671 2.000 1.292 1.664 1.990 1.290 1.660 1.984 1.282 1.646 1.962 1.282 1.645 1.960 80% 90% 95% Confidence Level 31.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.390 2.374 2.364 2.330 2.326 98% 63.66 318.31 636.62 9.925 22.327 31.599 5.841 10.215 12.924 4.604 7.173 8.610 4.032 5.893 6.869 3.707 5.208 5.959 3.499 4.785 5.408 3.355 4.501 5.041 3.250 4.297 4.781 3.169 4.144 4.587 3.106 4.025 4.437 3.055 3.930 4.318 3.012 3.852 4.221 2.977 3.787 4.140 2.947 3.733 4.073 2.921 3.686 4.015 2.898 3.646 3.965 2.878 3.610 3.922 2.861 3.579 3.883 2.845 3.552 3.850 2.831 3.527 3.819 2.819 3.505 3.792 2.807 3.485 3.768 2.797 3.467 3.745 2.787 3.450 3.725 2.779 3.435 3.707 2.771 3.421 3.690 2.763 3.408 3.674 2.756 3.396 3.659 2.750 3.385 3.646 2.704 3.307 3.551 2.660 3.232 3.460 2.639 3.195 3.416 2.626 3.174 3.390 2.581 3.098 3.300 2.576 3.090 3.291 99% 99.8% 99.9% 80 1001 10001 z