The following table contains the number of successes and failures for three categories of a variable. Test whether the proportions are equal for each category at the a = 0.05 level of significance. Category 1 Category 2 Category 3 5 Failures 37 36 60 Successes 67 41 63 Click the icon to view the Chi-Square table of critical values. Chi-Square Table Area to the Right of Critical Value Degrees of State the hypotheses. Choose the correct answer below. Freedom 0.995 0.99 0.975 0.95 0.90 0.10 0.05 0.025 0.01 0.00 0.004 0.016 2.706 3.841 5.024 6.635 O A. Ho The categories of the variable and success and failure are independent. 0.010 0.020 0.051 0.103 0.211 4.605 5.991 7.378 9.210 H1: The categories of the variable and success and failure are dependent 0.072 0.115 0.216 0.352 0.584 6.251 7.815 9.348 11.345 0.207 0.29 0.484 0.711 1.064 7.779 9.488 11.143 13.277 JAVIAWN 0.831 1.145 1.610 9.236 11.070 12.833 15.086 O B. Ho P1 = P2 = P3 0.412 0.554 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 H,: At least one of the proportions is different from the others. 0.989 1.239 1.690 2.167 2.833 12.017 14.067 16.013 18.475 1.344 1.646 2.180 2.733 3.490 13.362 15.507 17.535 20.090 O C. Ho: The categories of the variable and success and failure are dependent 1.735 2.088 2.700 3.325 4.168 14.684 16.919 19.023 21.666 H1: The categories of the variable and success and failure are independent 10 2.156 2.558 3.247 3.940 4.865 15.987 18.307 20.483 23.209 11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.920 24.725 O D. Ho Hy = E, and H2 = E2 and H3 = E3 12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 13 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 H, At least one mean is different from what is expected 14 4.075 4.660 5.629 6.571 7.790 21.064 23.685 26.119 29.141 4.601 5.229 6.262 7.261 8.547 22.307 24.996 27.488 30 578 5.142 5.812 6.908 7.962 9.312 23.542 26.296 28.845 32.000 5.697 6.408 7.564 8.672 10.085 24.769 27.587 30.191 33.409 6.265 7.015 8.231 9.390 10.865 25.989 28.869 31.526 34.805 6.844 7.633 8,907 10.117 11.651 27.204 30.144 32.852 36.191 7.434 8.260 9.591 10.851 12.443 28.412 31.410 34.170 37 566 8.034 8.897 10.283 11.591 13.240 29.615 32.671 35.479 38.932 8.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 40.289 9.260 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 42.980 10.520 11.524 13.120 14.611 16.473 34.382 37.652 40.646 44.314 11.160 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 11.808 12.879 14.573 16.151 18.114 36.741 40.113 43.195 46.963 12.461 13.565 15.308 16.928 18.939 37.916 41.337 44.461 48.278 13.121 14.256 16.047 17.708 19.768 39.087 42.557 45.722 49.588 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691
