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To test H0​: μ=100 versus H1​: μ≠​100, a simple random sample size of n=23 is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(d). (a) If x=105 and s=9.1​, compute the test statistic. ​(b) If the researcher decides to test this hypothesis at the α=0.01 level of​ significance, determine the critical values. (Use a comma to separate answers as needed. Round to three decimal places as​ needed.)

To test H0​: μ=100 versus H1​: μ≠​100, a simple random sample size of n=23 is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(d). (a) If x=105 and s=9.1​, compute the test statistic. ​(b) If the researcher decides to test this hypothesis at the α=0.01 level of​ significance, determine the critical values. (Use a comma to separate answers as needed. Round to three decimal places as​ needed.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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To test H0​: μ=100 versus H1​: μ≠​100, a simple random sample size of n=23 is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(d).

(a) If x=105 and s=9.1​, compute the test statistic.

​(b) If the researcher decides to test this hypothesis at the α=0.01 level of​ significance, determine the critical values. (Use a comma to separate answers as needed. Round to three decimal places as​ needed.) 

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 0.02 0.01 0.005 0.0025 0.001 0.0005 df 3.078 15.894 4.849 3.482 2.999 2.757 1.376 1.963 31.821 63.657 318.309 636.619 31.599 12.924 8.610 6.869 1 1.000 6.314 12.706 127.321 1 2.920 2.353 2.132 2.015 9.925 5.841 4.604 14.089 7.453 5.598 4.773 22.327 10.215 7.173 5.893 0.816 1.061 0.978 0.941 1.386 1.886 4.303 6.965 2 1.638 1.533 3 0.765 1.250 1.190 1.156 3.182 2.776 4.541 3.747 3 4 4 0.741 0.727 0.920 1.476 2.571 3.365 4.032 0.718 7 0.711 8 0.706 0.703 1.943 1.895 1.860 1.833 1.812 5.208 4.785 4.501 4.297 1.134 2.447 2.612 4.317 5.959 5.408 5.041 0.906 1.440 1.415 1.397 1.383 1.372 3.143 2.998 2.896 2.821 3.707 6. 0.896 0.889 0.883 1.119 1.108 1.100 1.093 2.517 2.449 2.398 2.359 3.499 3.355 3.250 3.169 4.029 3.833 3.690 3.581 2.365 2.306 7 8 2.262 2.228 4.781 4.587 9 10 0.700 0.879 2.764 4.144 10 0.876 0.873 0.870 1.088 1.363 1.796 1.782 1.771 1.761 1.753 3.106 3.055 3.012 3.497 3.428 3.372 4.025 3.930 3.852 3.787 3.733 11 4.437 0.697 0.695 0.694 0.692 2.201 2.179 2.160 2.328 2.718 11 12 13 1.083 1.079 1.356 1.350 2.303 2.282 2.264 2.681 2.650 2.624 2.602 4.318 4.221 12 13 2.145 2.131 2.977 2.947 14 0.868 1.076 1.345 3.326 3.286 4.140 14 15 0.691 0.866 1.074 1.341 2.249 4.073 15 3.686 3.646 3.610 3.579 3.552 16 17 0.690 0.689 0.688 0.688 0.687 0.865 0.863 0.862 1.071 1.069 1.067 1.337 1.333 1.330 1.328 1.746 1.740 2.120 2.110 2.235 2.224 2.214 2.205 2.583 2.567 2.921 2.898 2.878 3.252 3.222 4.015 3.965 3.922 16 17 1.734 1.729 18 2.101 2.552 3.197 18 3.883 3.850 19 0.861 1.066 2.093 2.539 2.861 3.174 19 20 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 20 0.686 0.686 0.685 0.685 0.859 0.858 0.858 21 22 1.063 1.061 1.323 1.321 1.319 1.721 1.717 2.080 2.074 2.189 2.183 2.177 2.172 2.167 2.518 2.508 3.527 3.505 3.485 2.831 2.819 3.135 3.119 3.819 3.792 3.768 3.745 3.725 21 22 1.060 1.059 1.058 2.069 2.064 2.060 2.500 2.492 2.485 2.807 2.797 2.787 23 1.714 3.104 23 0.857 0.856 3.091 3.078 3.467 3.450 24 1.318 1.711 24 25 0.684 1.316 1.708 25 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 26 Print Done parts remaining Clear All
Transcribed Image Text: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 0.02 0.01 0.005 0.0025 0.001 0.0005 df 3.078 15.894 4.849 3.482 2.999 2.757 1.376 1.963 31.821 63.657 318.309 636.619 31.599 12.924 8.610 6.869 1 1.000 6.314 12.706 127.321 1 2.920 2.353 2.132 2.015 9.925 5.841 4.604 14.089 7.453 5.598 4.773 22.327 10.215 7.173 5.893 0.816 1.061 0.978 0.941 1.386 1.886 4.303 6.965 2 1.638 1.533 3 0.765 1.250 1.190 1.156 3.182 2.776 4.541 3.747 3 4 4 0.741 0.727 0.920 1.476 2.571 3.365 4.032 0.718 7 0.711 8 0.706 0.703 1.943 1.895 1.860 1.833 1.812 5.208 4.785 4.501 4.297 1.134 2.447 2.612 4.317 5.959 5.408 5.041 0.906 1.440 1.415 1.397 1.383 1.372 3.143 2.998 2.896 2.821 3.707 6. 0.896 0.889 0.883 1.119 1.108 1.100 1.093 2.517 2.449 2.398 2.359 3.499 3.355 3.250 3.169 4.029 3.833 3.690 3.581 2.365 2.306 7 8 2.262 2.228 4.781 4.587 9 10 0.700 0.879 2.764 4.144 10 0.876 0.873 0.870 1.088 1.363 1.796 1.782 1.771 1.761 1.753 3.106 3.055 3.012 3.497 3.428 3.372 4.025 3.930 3.852 3.787 3.733 11 4.437 0.697 0.695 0.694 0.692 2.201 2.179 2.160 2.328 2.718 11 12 13 1.083 1.079 1.356 1.350 2.303 2.282 2.264 2.681 2.650 2.624 2.602 4.318 4.221 12 13 2.145 2.131 2.977 2.947 14 0.868 1.076 1.345 3.326 3.286 4.140 14 15 0.691 0.866 1.074 1.341 2.249 4.073 15 3.686 3.646 3.610 3.579 3.552 16 17 0.690 0.689 0.688 0.688 0.687 0.865 0.863 0.862 1.071 1.069 1.067 1.337 1.333 1.330 1.328 1.746 1.740 2.120 2.110 2.235 2.224 2.214 2.205 2.583 2.567 2.921 2.898 2.878 3.252 3.222 4.015 3.965 3.922 16 17 1.734 1.729 18 2.101 2.552 3.197 18 3.883 3.850 19 0.861 1.066 2.093 2.539 2.861 3.174 19 20 0.860 1.064 1.325 1.725 2.086 2.197 2.528 2.845 3.153 20 0.686 0.686 0.685 0.685 0.859 0.858 0.858 21 22 1.063 1.061 1.323 1.321 1.319 1.721 1.717 2.080 2.074 2.189 2.183 2.177 2.172 2.167 2.518 2.508 3.527 3.505 3.485 2.831 2.819 3.135 3.119 3.819 3.792 3.768 3.745 3.725 21 22 1.060 1.059 1.058 2.069 2.064 2.060 2.500 2.492 2.485 2.807 2.797 2.787 23 1.714 3.104 23 0.857 0.856 3.091 3.078 3.467 3.450 24 1.318 1.711 24 25 0.684 1.316 1.708 25 26 0.684 0.856 1.058 1.315 1.706 2.056 2.162 2.479 2.779 3.067 3.435 3.707 26 Print Done parts remaining Clear All
t-Distribution Area in Right Tail 0.688 0.687 1.328 1.325 2.093 2.086 1.729 2.205 2.197 2.539 2.528 19 0.861 0.860 1.066 2.861 3.174 3.579 3.883 19 20 1.064 1.725 2.845 3.153 3.552 3.850 20 0.859 0.858 0.858 1.063 1.061 1.060 1.059 1.058 1.323 1.321 1.319 2.080 2.074 2.069 2.064 2.060 2.518 2.508 2.500 2.492 2.485 21 22 0.686 0.686 1.721 1.717 1.714 2.189 2.183 2.177 2.172 2.167 2.831 2.819 2.807 2.797 2.787 3.135 3.119 3.527 3.505 3.485 3.467 3.450 3.819 3.792 3.768 21 22 0.685 0.685 0.684 3.104 3.091 23 23 0.857 0.856 1.318 1.316 1.711 1.708 24 3.745 24 25 3.078 3.725 25 1.706 1.703 1.058 1.057 1.056 1.055 1.055 2.056 2.052 2.048 2.479 2.473 0.856 0.855 0.855 3.435 3.421 3.408 3.396 3.385 26 0.684 1.315 2.162 2.779 3.067 3.057 3.047 3.038 3.030 3.707 26 1.314 1.313 1.311 1.310 2.158 2.154 2.150 2.147 27 0.684 2.771 3.690 27 0.683 0.683 0.683 28 1.701 2.467 2.763 3.674 3.659 3.646 28 29 30 0.854 0.854 1.699 1.697 2.045 2.042 2.462 2.457 2.756 2.750 29 30 1.696 1.694 1.692 1.691 1.690 3.633 3.622 1.054 2.453 3.022 3.015 3.375 3.365 3.356 3.348 3.340 31 0.682 0.853 0.853 0.853 0.852 0.852 1.309 2.040 2.037 2.035 2.032 2.030 2.144 2.141 2.138 2.136 2.133 2.744 2.738 2.733 2.728 2.724 31 0.682 0.682 0.682 0.682 32 1.054 1.309 2.449 2.445 2.441 2.438 32 1.053 1.052 1.052 33 1.308 3.008 3.611 33 34 35 1.307 1.306 3.002 2.996 3.601 3.591 34 35 2.028 2.026 2.024 2.023 2.021 1.052 2.131 2.719 2.715 2.712 2.708 2.704 2.990 2.985 2.980 2.976 3.582 3.574 36 0.681 0.852 0.851 0.851 0.851 1.306 1.688 1.687 1.686 1.685 1.684 2.434 3.333 36 3.326 3.319 3.313 3.307 37 0.681 1.051 1.305 2.129 2.431 37 38 39 0.681 0.681 0.681 1.051 1.050 1.050 1.304 1.304 3.566 3.558 3.551 2.127 2.429 38 39 2.125 2.426 2.423 2.123 40 0.851 1.303 2.971 40 0.849 0.848 0.847 0.846 0.846 1.047 1.299 2.009 2.000 2.403 2.390 2.381 2.374 2.368 2.678 2.660 2.648 2.639 2.632 50 0.679 1.676 3.261 2.109 2.099 2.093 2.088 2.084 2.937 3.496 50 0.679 1.045 1.296 1.67 2.91. 3.460 3.23 3.211 3.195 60 60 0.678 0.678 0.677 3.435 3.416 3.402 70 1.044 1.294 1.043 1.292 1.042 1.291 1.667 1.664 1.662 1.994 1.990 2.899 2.887 2.878 70 80 80 90 1.987 3.183 90 100 1000 1.290 1.282 1.282 2.626 2.581 2.576 3.174 3.098 3.090 0.845 1.660 1.646 1.645 2.081 3.390 0.677 0.675 0.674 1.042 1.984 1.962 1.960 2.364 2.330 2.326 2.871 2.813 2.807 100 0.842 0.842 1.037 1.036 2.056 2.054 3.300 1000 3.291 z df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0,005 0.0025 0.001 0.0005 df Print Done parts remaining Clear All
Transcribed Image Text:t-Distribution Area in Right Tail 0.688 0.687 1.328 1.325 2.093 2.086 1.729 2.205 2.197 2.539 2.528 19 0.861 0.860 1.066 2.861 3.174 3.579 3.883 19 20 1.064 1.725 2.845 3.153 3.552 3.850 20 0.859 0.858 0.858 1.063 1.061 1.060 1.059 1.058 1.323 1.321 1.319 2.080 2.074 2.069 2.064 2.060 2.518 2.508 2.500 2.492 2.485 21 22 0.686 0.686 1.721 1.717 1.714 2.189 2.183 2.177 2.172 2.167 2.831 2.819 2.807 2.797 2.787 3.135 3.119 3.527 3.505 3.485 3.467 3.450 3.819 3.792 3.768 21 22 0.685 0.685 0.684 3.104 3.091 23 23 0.857 0.856 1.318 1.316 1.711 1.708 24 3.745 24 25 3.078 3.725 25 1.706 1.703 1.058 1.057 1.056 1.055 1.055 2.056 2.052 2.048 2.479 2.473 0.856 0.855 0.855 3.435 3.421 3.408 3.396 3.385 26 0.684 1.315 2.162 2.779 3.067 3.057 3.047 3.038 3.030 3.707 26 1.314 1.313 1.311 1.310 2.158 2.154 2.150 2.147 27 0.684 2.771 3.690 27 0.683 0.683 0.683 28 1.701 2.467 2.763 3.674 3.659 3.646 28 29 30 0.854 0.854 1.699 1.697 2.045 2.042 2.462 2.457 2.756 2.750 29 30 1.696 1.694 1.692 1.691 1.690 3.633 3.622 1.054 2.453 3.022 3.015 3.375 3.365 3.356 3.348 3.340 31 0.682 0.853 0.853 0.853 0.852 0.852 1.309 2.040 2.037 2.035 2.032 2.030 2.144 2.141 2.138 2.136 2.133 2.744 2.738 2.733 2.728 2.724 31 0.682 0.682 0.682 0.682 32 1.054 1.309 2.449 2.445 2.441 2.438 32 1.053 1.052 1.052 33 1.308 3.008 3.611 33 34 35 1.307 1.306 3.002 2.996 3.601 3.591 34 35 2.028 2.026 2.024 2.023 2.021 1.052 2.131 2.719 2.715 2.712 2.708 2.704 2.990 2.985 2.980 2.976 3.582 3.574 36 0.681 0.852 0.851 0.851 0.851 1.306 1.688 1.687 1.686 1.685 1.684 2.434 3.333 36 3.326 3.319 3.313 3.307 37 0.681 1.051 1.305 2.129 2.431 37 38 39 0.681 0.681 0.681 1.051 1.050 1.050 1.304 1.304 3.566 3.558 3.551 2.127 2.429 38 39 2.125 2.426 2.423 2.123 40 0.851 1.303 2.971 40 0.849 0.848 0.847 0.846 0.846 1.047 1.299 2.009 2.000 2.403 2.390 2.381 2.374 2.368 2.678 2.660 2.648 2.639 2.632 50 0.679 1.676 3.261 2.109 2.099 2.093 2.088 2.084 2.937 3.496 50 0.679 1.045 1.296 1.67 2.91. 3.460 3.23 3.211 3.195 60 60 0.678 0.678 0.677 3.435 3.416 3.402 70 1.044 1.294 1.043 1.292 1.042 1.291 1.667 1.664 1.662 1.994 1.990 2.899 2.887 2.878 70 80 80 90 1.987 3.183 90 100 1000 1.290 1.282 1.282 2.626 2.581 2.576 3.174 3.098 3.090 0.845 1.660 1.646 1.645 2.081 3.390 0.677 0.675 0.674 1.042 1.984 1.962 1.960 2.364 2.330 2.326 2.871 2.813 2.807 100 0.842 0.842 1.037 1.036 2.056 2.054 3.300 1000 3.291 z df 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0,005 0.0025 0.001 0.0005 df Print Done parts remaining Clear All
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