10.3

3. To test H0: p = 60 versus H1: u

3. To test Ho: = 60 versus HI : g < 60, a random sample of size n = 24 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. 5 Click here to view the t-Distribution Area in Right Tail. (a) If x = 56.7 and s = 12.9, compute the test statistic. to = (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the = 0.05 level of significance, determine the critical value(s). Although technology or a t-distribution table can be used to find the critical value, in this problem use the t-distribution table given. Critical Value: (Round to three decimal places. Use a comma to separate answers as needed.) (c) Draw a t-distribution that depicts the critical region. Choose the correct answer below. oc. -ta/2 (d) Will the researcher reject the null hypothesis? C) A. No, because the test statistic falls in the critical region. C) B. No, because the test statistic does not fall in the critical region. C) C. Yes, because the test statistic falls in the critical region. C) D. Yes, because the test statistic does not fall in the critical region. 5: t-Distribution Area in Right Tail t-Distribution Area in Right Tail 2 3 4 s 6 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 23 24 26 27 29 30 31 32 34 37 38 39 40 so 60 70 80 90 100 1000 0.25 1.000 0816 0.765 0.741 o. 727 0.718 0.711 0.706 o. 703 0.700 0.697 0.695 0.694 0.692 0.691 0.689 0.688 0.688 0.687 0.686 0.686 0.685 0.684 0.684 0.684 0.683 0.6*2 0.682 0.682 0.682 0.682 0.681 0.681 0.681 0.681 0.681 0.679 0.679 0.678 0.678 0.677 0.677 0.675 0.674 0.20 1376 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 O.M5 0.863 0.862 0.861 0.860 0.859 085* 0858 0S57 0856 0856 0S55 0.854 0.854 0.853 0.853 0.853 0.852 0.852 0.852 0.851 0.851 0.851 0.851 0.849 0.848 0.847 0.846 0.846 0.845 0.842 0.842 0.15 1.963 1.386 1.250 I.I') 1.156 1.134 1.119 1. ICN 1.100 1093 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 1.05* 1.058 1.057 1056 1.055 1.055 1.054 1.054 1.053 1.052 1.052 1.052 1051 1.051 1.050 1.050 1.047 1.045 1.044 1.043 1.042 1.042 1.037 1.036 0.10 3.078 1.886 1.638 1.533 1476 1 A40 1415 1397 1372 1363 1356 1350 1345 1337 1333 1328 1325 1323 1321 1319 1318 1.316 1.315 1.314 1.313 1311 1310 1309 1309 1308 1307 1305 1304 1304 1299 1296 1294 1292 1291 1290 1282 1282 0.05 6314 2.920 2.353 2132 2.015 1.943 1.895 1.&60 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1699 1.697 1.696 1.694 1.692 1.691 1.690 1.6B* Its 1.686 1.685 1.684 1.676 1.671 1.667 1.664 1.662 1.660 1.646 1.645 0.025 12.706 4.303 3.182 2.776 2.571 2447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.(kS6 2.cvso 2.074 2.h9 2.064 2.cro 2.056 2.(62 2048 2045 2042 2040 2037 2035 2032 2.030 2.028 2.026 2.024 2.023 2.021 2.009 2.000 1.994 1.990 1.987 1.984 1.962 1.960 0.02 15.894 4.849 2.999 2.757 2.612 2.517 2.449 2.398 2359 2.328 2.303 2282 2.264 2249 2.235 2.224 2.214 2.197 2.189 2.183 2.177 2.172 2.167 2.162 2.158 2.154 2.150 2.147 2.144 2.141 2.138 2.136 2.133 2.131 2.129 2.127 2.125 2.123 2.109 2.099 2.093 2.cvu 2.(81 2.056 2.054 0.01 31.821 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 2328 2518 2-508 2-500 N92 2.485 2.479 2473 2467 2.462 2.457 2.453 2.449 2.445 2.441 2.438 2.434 2.431 2.429 2.426 2.423 2.403 2390 2381 2374 2.368 2364 2.330 2.326 0.005 63.657 9.925 5.841 4.032 3.707 3.499 3.355 3.250 3.169 3.106 3.055 3.012 2977 2.947 2.921 2.898 2.878 2.861 2.845 2.831 2.819 2.807 2.797 2.787 2.779 2.771 2.763 2.756 2.750 2.744 2.738 2.733 2.728 2.724 2.719 2.715 2.712 2.708 2.704 2.678 2.660 2.648 2.639 2632 2626 2.581 2.576 0.0025 127.321 14.(B9 7.453 5.598 4.773 4.317 4.029 3.833 3.690 3.581 3.497 3.428 3.372 3.326 3286 3.252 3.222 3.197 3.174 3.153 3.135 3.119 3.104 3.091 3.078 3.067 3.057 3.047 3.038 3.030 3.022 3.015 3.0(B 3.002 2.996 2.990 2.985 2.980 2.976 2.971 2.937 2.915 2.899 2.887 2878 2871 2.813 2.807 0.001 318.309 22.327 10.215 7.173 5.893 5.208 4.75 4.501 4.297 4.144 4.025 3.930 3852 3.787 3.733 3.6M 3.646 3.610 3.579 3.552 3.527 3.5(F 3.485 3467 3450 3.435 3421 3.408 3.396 3.385 3.375 3.3s 3.356 3.348 3.340 3.333 3.326 3.319 3.313 3.307 3.261 3.232 3.211 3.195 3.183 3.174 3.098 3.090 ta/2 0.0005 636.619 31.599 12.924 8.610 6.869 5.959 5.408 5.041 4.781 4.587 4.437 4318 421 4.140 4.073 4.015 3.965 3.922 3850 3819 3.792 3.768 3.745 3.725 3.707 3690 3.674 3.659 3.646 3.633 3.622 3.611 3.601 3.591 3.582 3.574 3.566 3.558 3.551 3.496 3.460 335 3.416 3402 3390 3.300 3291