Determine (a) the ²₀ teststatistic, (b) the degrees offreedom, (c) theP-value, and (d) test the hypothesis at the =0.05 level of significance.

H0: The random variable X is binomial with n=4, p=0.8

H1: The random variable X is not binomial with n=4, p= 0.8

X 0 1 2 3 4

Observed 5 39 121 437 387

Expected 1.6 25.3 151.9 405.1 405.1

Chi-Square ( Chi Squared ) Distribution Area to the Right of Critical Value Degrees of Freedom .995 0.99 0.975 0.95 0.9 0.1 .05 0.025 0.01 0.005 Degrees of Freedom 0.001 0.004 0.016 2.706 3.841 5.024 5.635 7.879 0.01 .02 .051 .103 0.211 4.605 5.991 7.378 9.21 10.597 0.072 0.115 0.216 0.352 0.584 5.251 7.815 9.348 11.345 12.838 w 0.207 0.297 .484 .711 1.064 7.77 9.488 11.143 13.277 14.86 0.412 0.554 0.831 1.145 1.61 .236 11.07 12.833 15.086 16.75 6 4 DO V G UI A W N H 0.676 0.872 1.237 1.635 2.204 10.645 12.592 14.449 16.812 18.548 0.989 1.239 . 69 2.167 2.833 12.017 14.067 16.013 18.475 20.278 1.344 1.646 2.18 2.733 3.49 13.362 15.507 17.535 20.09 21.955 8 1.735 2.08 2.7 3.325 4.168 14.684 16.919 19.023 21.666 23.589 9 2.15 2.558 3.247 3.94 4.86 15.987 18.307 20.483 23.209 25.188 10 11 2.603 3.053 3.816 4.575 5.578 17.275 19.675 21.92 24.725 26.757 11 12 3.074 3.571 4.404 5.226 6.304 18.549 21.026 23.337 26.217 28.3 12 13 3.565 4.107 5.009 5.892 7.042 19.812 22.362 24.736 27.688 29.819 13 14 4.075 4.6 5.629 6.571 7.79 21.064 23.685 26.119 29.141 31.319 14 15 4.601 5.229 5.262 7.261 8.547 22.307 24.996 27.488 30.578 32.801 15 16 5.142 5.812 6.908 .962 9.312 23.542 26.296 28.845 32 34.267 16 17 5.697 5.408 7.564 3.672 10.085 24.769 27.587 30.191 33.409 35.718 17 18 5.265 7.015 3.231 9.39 10.86 25.989 28.869 31.526 34.805 37.156 18 19 5.844 7.633 8.907 10.117 11.651 27.204 30.144 32.852 36.191 38.582 19 20 7.434 8.26 9.591 10.851 12.443 28.412 31.4 34.17 37.566 39.997 20 21 8.034 8.897 10.283 11.591 13.2 29.615 32.671 35.479 38.932 41.401 21 22 3.643 9.542 10.982 12.338 14.041 30.813 33.924 36.781 10.289 42.796 22 23 1.26 10.196 11.689 13.091 14.848 32.007 35.172 38.076 41.638 44.181 23 24 9.886 10.856 12.401 13.848 15.659 33.196 36.415 39.364 12.98 45.559 24 25 10.52 11.524 13.1 14.611 16.473 34.382 37.652 40.646 44.314 46.928 25 26 11.16 12.198 13.844 15.379 17.292 35.563 38.885 41.923 45.642 48.29 27 11.808 12.879 14.573 16.151 18.114 36.741 40.113 195 46.963 19.645 27 28 12.461 13.565 15.308 16.928 18.939 37.916 41.337 14.461 48.278 50.993 28 29 13.121 14.256 16.047 17.708 19.768 39.087 42.557 15.722 49.588 52.336 29 30 13.787 14.953 16.791 18.493 20.599 40.256 43.773 46.979 50.892 53.672 30 40 20.707 22.164 24.433 26.509 29.051 51.805 55.758 59.342 63.691 66.766 40 50 27.991 29.707 32.357 34.764 37.689 63.167 67.505 71.42 76.154 79.49 50 60 35.534 37.485 40.482 43.188 46.459 74.397 79.082 83.298 88.379 91.952 60 70 43.275 45.442 48.758 51.739 55.329 85.527 90.531 95.023 100.425 104.215 70 80 51.172 53.54 57.153 50.391 64.278 96.578 101.879 106.629 112.329 116.321 30 90 59.196 61.754 65.647 69.126 73.291 107.565 113.145 118.136 124.116 128.299 100 67.328 70.065 74.222 77.929 82.358 118.498 124.342 129.561 135.807 140.169 100 egrees of Freedom .995 0.99 0.975 0.95 0.9 0.1 .05 .025 0.01 0.005 Degrees of Freedom