10.3

Distribution Area in Right Tail 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 if 1.00 1.376 1.963 3.078 6.314 12.706 15.894 31.821 63.657 127.321 318.309 636.619 0.816 1.061 1.386 1.886 2.920 4.303 4.849 6.965 9.925 14.089 22.327 31.599 0.978 1.250 1.638 2.353 3.182 3.482 4.541 5.841 7.453 10.215 12.924 0.765 0.741 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 7.173 8.610 0.920 1.156 2.015 2.571 2.757 3.365 4.032 4.773 5.893 1.476 6.869 0.727 5.959 0.718 0.90 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 0.711 4.501 5.041 0.706 0.889 1.108 1.397 1.860 2.306 2.449 2.896 3.355 .833 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 0.700 0.87 1.093 4.587 11 0.697 0.876 1.088 1.363 1.796 2.201 2.328 2.718 3.10 3.497 4.025 4.437 1.083 1.356 1.782 2.179 2.303 2.681 3.055 3.428 3.930 4.318 0.695 0.873 4.221 0.694 0.870 1.079 350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 0.692 0.868 1.076 1.34 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 0.691 0.866 1.074 1.34 1.753 2.131 2.249 2.602 2.947 3.286 3.733 4.073 0.690 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.015 3.222 3.646 3.965 0.689 0.863 .069 1.333 1.740 2.110 2.224 2.898 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 0.861 1.328 1.729 2.093 2.205 2.539 2.861 3.174 3.579 3.883 0.68 1.066 0.687 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 3.850 0.686 0.859 1.063 .323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 3.505 3.792 0.686 0.858 1.061 1.321 1.717 2.074 2.183 2.508 2.819 3.119 0.685 0.858 1.060 1.319 1.714 2.069 2.177 2.500 2.807 3.104 3.485 3.768 0.685 1.318 2.064 2.172 2.797 3.091 3.467 0.857 .059 1.711 2.492 3.745 0.684 0.856 1.058 1.316 1.708 2.06 2.167 2.485 2.787 3.450 3.725 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 3.690 0.684 0.855 1.057 1.314 1.703 2.052 2.158 2.473 2.771 3.057 3.421 0.683 0.855 1.056 1.313 1.701 2.048 2.154 2.467 2.763 3.047 3.408 3.674 3.038 3.396 3.659 0.683 0.854 1.055 1.311 1.699 2.045 2.150 2.462 2.756 0.68 0.854 1.055 1.310 1.697 2.042 2.147 2.457 2.750 3.03 3.385 3.646 0.682 0.853 1.054 1.309 1.696 2.040 2.144 2.453 2.744 3.022 3.375 3.63 0.682 0.853 1.054 309 1.694 2.037 2.141 2.449 2.738 3.015 3.365 3.622 3.356 3.611 0.682 0.85 1.053 1.308 1.692 2.035 2.138 2.445 2.733 3.008 0.682 0.852 1.052 1.307 1.691 2.032 2.136 2.441 2.728 3.002 3.348 3.601 3.591 0.682 0.852 1.052 1.306 1.690 2.030 2.133 2.438 2.724 2.996 3.340 0.681 0.852 1.052 1.306 1.688 2.028 2.131 2.434 2.719 2.990 3.333 3.582 3.326 3.574 0.681 0.851 1.051 1.305 1.687 2.026 2.129 2.431 2.715 2.985 0.681 0.851 1.051 1.304 1.686 2.024 2.127 2.429 2.712 2.980 3.319 3.566 3.313 3.558 0.68 0.851 1.050 1.304 1.685 2.023 2.125 2.426 2.708 2.976 0.681 0.851 1.050 1.303 1.684 2.021 2.123 2.423 2.704 2.971 3.307 3.551 0.679 0.849 1.676 2.009 2.109 2.403 2.678 2.937 3.261 3.496 1.047 1.299 0.848 1.296 1.671 2.000 2.099 2.390 2.660 2.915 3.232 0.679 1.045 3.460 0.847 .044 1.294 1.667 1.994 2.093 2.381 2.648 2.899 3.211 3.435 0.678 2.639 2.887 3.195 80 3.416 0.678 0.846 1.292 1.664 1.990 2.088 2.374 90 3.402 0.677 0.846 1.042 1.291 1.662 1.987 2.084 2.368 2.632 2.878 3.183 0.677 0.845 1.290 1.660 1.984 2.081 2.364 2.626 2.871 3.174 3.390 100 1.042 0.675 0.842 1.037 1.282 1.646 1.962 2.056 2.330 2.581 2.813 3.098 3.300 1000 z 0.674 0.842 1.036 1.282 1.645 1.960 2.054 2.326 2.576 2.807 3.090 3.291 To test Ho: H = 100 versus H1: H # 100, a simple random sample of size n = 20 is obtained from a population that is known to be normally distributed. Answer parts (a)-(e). 13 Click here to view the t-Distribution Area in Right Tail. (a) If x = 104.9 and s = 9.9, compute the test statistic. t= (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a = 0.01 level of significance, determine the critical values. The critical value(s) is/are (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Draw a t-distribution that depicts the critical region(s). Which of the following graphs shows the critical region(s) in the t-distribution? O A. B. O C. Q (d) Will the researcher reject the null hypothesis? A. The researcher will reject the null hypothesis since the test statistic is in the rejection region. O B. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is in the rejection region. O C. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not in the rejection region. D. The researcher will reject the null hypothesis since the test statistic is not in the rejection region. (e) Construct a 99% confidence interval to test the hypothesis. The confidence interval is ( (Round to two decimal places as needed.) in the interval. (1) Ho based on the confidence interval because the hypothesized value u = 100 (2) 13: t-Distribution Area in Right Tail t-Distribution Area in Right Tail df 0.25 0.20 0.15 0.10 0.05 0.025 ).02 0.01 0.005 0.0025 0.001 0.0005 df 127.321 318.309 636.619 1.000 1.376 1.963 3.078 6.314 12.706 15.894 31.821 63.65 1.386 1.886 2.920 4.303 4.849 6.96 9.925 14.089 22.327 31.599 0.816 1.061 1.250 1.638 2.353 3.182 3.482 4.541 5.841 10.215 12.924 0.765 0.978 7.453 DIANNE 0.941 1.190 1.533 2.132 2.776 2.999 3.747 4.604 5.598 7.173 8.610 0.741 0.727 0.920 1.15 1.476 2.015 2.571 2.757 3.36 4.032 4.773 5.893 6.86 SONOMAWINE 5.959 0.718 0.906 1.134 1.440 1.943 2.447 2.612 3.143 3.707 4.317 5.208 0.71 0.896 1.119 1.415 1.895 2.365 2.517 2.998 3.499 4.029 4.785 5.408 0.706 0.889 1.106 1.397 1.860 2.306 2.449 2.896 3.355 3.833 4.501 5.041 0.703 0.883 1.100 1.383 1.833 2.262 2.398 2.821 3.250 3.690 4.297 4.781 10 0.879 1.093 1.372 1.812 2.228 2.359 2.764 3.169 3.581 4.144 4.587 10 0.700 1.363 1.796 2.20 2.328 2.718 3.106 3.497 4.025 4.437 11 11 0.697 0.876 1.088 0.695 0.873 1.083 1.356 1.78 2.179 2.303 2.681 3.055 3.428 3.930 318 12 0.694 0.870 1.079 1.350 1.771 2.160 2.282 2.650 3.012 3.372 3.852 4.221 13 0.692 0.868 1.076 1.345 1.761 2.145 2.264 2.624 2.977 3.326 3.787 4.140 14 341 1.753 2.13 2.249 2.602 2.947 3.286 3.733 4.073 15 15 0.691 0.860 1.074 16 0.69 0.865 1.071 1.337 1.746 2.120 2.235 2.583 2.921 3.252 3.686 4.01 16 17 0.689 0.863 1.069 1.333 2110 2.224 2.898 3.222 3.646 3.965 1.740 2.567 17 18 0.688 0.862 1.067 1.330 1.734 2.101 2.214 2.552 2.878 3.197 3.610 3.922 18 2.093 2.205 2.539 2.861 3.174 3.579 3.883 19 19 0.688 0.861 1.066 1.328 1.729 20 20 0.687 0.860 3.850 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 3.552 1.063 1.323 1.721 2.080 2.189 2.518 2.831 3.135 3.527 3.819 21 21 0.686 0.859