Consider a multinomial experiment with n: 400 and k=3. The null hypothesis is H0: p1 = 0.60, p2 = 0.25, and p3 = 0.15. The observed frequencies resulting from the experiment are: (You may nd it useful to reference the appropriate table: chi-square table or F table) Category 1 2 3 Frequency 250 94 56 a. Choose the appropriate alternative hypothesis. 0 All population proportions differ from their hypothesized values. 0 At least one of the population proportions differs from its hypothesized value. b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and nal answer to 3 decimal places.) Test statistic _ You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test this claim, you roll the die 200 times and obtain the following frequencies: (You may find it useful to reference the appropriate table: guare table or F table) Click here for the Excel Data File Category 1 2 3 4 5 6 Frequency 40 35 33 30 33 29 3. Choose the appropriate alternative hypothesis to test if the population proportions differ. 0 All population proportions differ from 1/6. 0 Not all population proportions are equal to 1/6. b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) TABLE 3 x (Chi-Square) Distribution Entries in this table provide the values of Zany that correspond to a given upper-tail area a and a specified number of degrees of freedom df. For example, for a = 0.05 and df = 10, P( Zio 2 18.307) = 0.05. Area In Upper Tall, a a df 0.995 0.990 0.975 0.950 0.900 0.100 0.050 0.025 0.010 0.005 0.000 0.000 0.001 0.004 0.016 2.706 3.841 5.024 6.635 7.879 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 10.597 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 12.838 0.207 0.297 0.484 0.711 1.064 7.779 9.488 11.143 13.277 14.860 0.412 0.554 0.831 1.145 1.610 9.236 11.070 12.833 15.086 16.750 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 20.278 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 21.955 1 00 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 23.589 10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 25.188 11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 26.757 12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.300 13 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 29.819 14 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 31.319 15 4.601 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30.578 32.801 16 5.142 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 34.267 17 5.697 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 35.718 18 6.265 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 37.156 19 6.844 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 38.582 20 7.434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37.566 39.997 21 8.034 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 41.401 22 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 42.796 23 9.260 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 44.181 24 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 45.559 25 10.520 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 46.928 26 11.160 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.290 27 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 49.645 28 12.461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 50.993 29 13.121 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 52.336 30 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.672 31 14.458 15.655 17.539 19.281 21.434 41.422 44.985 48.232 52.191 55.003 32 15.134 16.362 18.291 20.072 22.271 42.585 46.194 49.480 53.486 56.328 33 15.815 17.074 19.047 20.867 23.110 43.745 47.400 50.725 54.776 57.648 34 16.501 17.789 19.806 21.664 23.952 44.903 48.602 51.966 56.061 58.964 35 17.192 18.509 20.569 22.465 24.797 46.059 49.802 53.203 57.342 60.275 36 17.887 19.233 21.336 23.269 25.643 47.212 50.998 54.437 58.619 61.581 37 18.586 19.960 22.106 24.075 26.492 48.363 52.192 55.668 59.893 62.883 38 19.289 20.691 22.878 24.884 27.343 49.513 53.384 56.896 61.162 64.181 39 19.996 21.426 23.654 25.695 28.196 50.660 54.572 58.120 62.428 65.476 40 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 66.766 41 21.421 22.906 25.215 27.326 29.907 52.949 56.942 60.561 64.950 68.053 42 22.138 23.650 25.999 28.144 30.765 54.090 58.124 61.777 66.206 69.336 43 22.859 24.398 26.785 28.965 31.625 55.230 59.304 62.990 67.459 70.616 44 23.584 25.148 27.575 29.787 32.487 56.369 60.481 64.201 68.710 71.893 45 24.311 25.901 28.366 30.612 33.350 57.505 61.656 65.410 69.957 73.166 46 25.041 26.657 29.160 31.439 34.215 58.641 62.830 66.617 71.201 74.437 47 25.775 27.416 29.956 32.268 35.081 59.774 64.001 67.821 72.443 75.704 48 26.511 28.177 30.755 33.098 35.949 60.907 65.171 69.023 73.683 76.969 49 27.249 28.941 31.555 33.930 36.818 62.038 66.339 70.222 74.919 78.231 50 27.991 29.707 32.357 34.764 37.689 63.167 67.505 71.420 76.154 79.490 55 31.735 33.570 36.398 38.958 42.060 68.796 73.311 77.380 82.292 85.749 60 35.534 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 91.952 65 39.383 41.444 44.603 47.450 50.883 79.973 84.821 89.177 94.422 98.105 70 43.275 45.442 48.758 51.739 55.329 85.527 90.531 95.023 100.425 104.215 75 47.206 49.475 52.942 56.054 59.795 91.061 96.217 100.839 106.393 1 10.286 80 51.172 53.540 57.153 60.391 64.278 96.578 101.879 106.629 112.329 116.321 85 55.170 57.634 61.389 64.749 68.777 102.079 107.522 112.393 118.236 122.325 90 59.196 61.754 65.647 69.126 73.291 107.565 113.145 118.136 124.116 128.299 95 63.250 65.898 69.925 73.520 77.818 113.038 118.752 123.858 129.973 134.247 100 67.328 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 140.169