lILJUIIIILJINZ 1 I You roll a die 62 times and record the outcome in the following table. The goal is to use a Chi-Square test to see if the die is fair. Chi-square (x 1} distribution Area In the right of critical value Degrees of freedom 0.995 0.99 0.9?5 0.95 0.90 0.10 0.05 0.025 0.01 0.005 1 0.001 0.004 0.016 2.?06 3.341 5.024 6.635 ?.3?9 2 0.010 0.020 0.051 0.103 0.211 4.605 5.991 ?.3?3 9.210 10.59? 3 0.0?2 0.115 0.216 0.352 0.534 6.251 ?.315 9.343 11.345 12.333 4 0.20? 0.29? 0.434 0.?11 1.064 ?.??9 9.433 11.143 13.2?? 14.360 5 0.412 0.554 0.331 1.145 1.610 9.236 11.0?1 12.333 15.036 16.?50 6 0.6?6 0.3?2 1.23? 1.635 2.204 10.645 12.592 14.449 16.312 13.543 7 0.939 1.239 1.690 2.16? 2.333 12.01? 14.06? 16.013 13.4?5 20.2?3 3 1.344 1.646 2.130 2.?33 3.490 13.362 15.50? 1?.535 20.090 21.955 9 1.?35 2.033 2.?111 3.325 4.163 14.634 16.919 19.023 21.666 23.539 10 2.156 2.553 3.24? 3.940 4.365 15.93? 13.30? 20.433 23.209 25.133 11 2.603 3.053 3.316 4.5?5 5.5?3 1?.2?5 19.6?5 21.920 24.?25 26.?5? 12 3.0?4 3.5?1 4.404 5.226 6.304 13.549 21 .026 23.33? 26.21? 23.299 13 3.565 4.10? 5.009 5.392 ?.042 19.312 22.362 24.?36 2?.633 29.319 14 4.0?5 4.660 5.629 6.5?1 ?.?90 21.064 23.635 26.1 19 29.141 31.319 15 4.601 5.229 6.262 ?.261 3.54? 22.30? 24.996 2? .433 30.5?3 32.301 16 5.142 5.312 6.903 ?.962 9.312 23.542 26.296 23.345 32.000 34.26? 1'? 5.69? 6.403 ?.564 3.6?2 10.035 24.?69 2?.53? 30.191 33.409 35.?13 13 6.265 ?.015 3.231 9.390 10.365 25.939 23.369 31.526 34.305 3?.156 19 6.344 ?.633 3.90? 10.11? 11.651 2?.204 30.144 32.352 36.191 33.532 20 ?.434 3.260 9.591 10.351 12.443 23.412 31.410 34.1?0 3?.566 39.99? 21 3.034 3.39? 10.233 11.591 13.240 29.615 32.6?1 35.4?9 33.932 41.401 22 3.643 9.542 10.932 12.333 14.042 30.313 33.924 36.?31 40.239 42.?96 23 9.260 10.196 11.639 13.091 14.343 32.00? 35.1?2 33.0?6 41.633 44.131 24 9.336 10.356 12.401 13.343 15.659 33.196 36.415 39.364 42.930 45.559 25 10.520 11.524 13.120 14.611 16.4?3 34.332 3? .652 40.646 44.314 46.923 26 11.160 12.193 13.344 15.3?9 1?.292 35.563 33.335 41.923 45.642 43.290 2? 11.303 12.3?9 14.5?3 16.151 13.114 36.?41 40.113 43.194 46.963 49.645 23 12.461 13.565 15.303 16.923 13.939 3?.916 41.33? 44.461 43.2?3 50.993 29 13.121 14.3? 16.04? 1?.?03 19.?63 39.03? 42.55? 45.?22 49.533 52.336 30 13.?3? 14954 16.?91 13.493 20.599 40.256 43.??3 46.979 50.392 53.6?2 40 20.?0? 22.164 24.433 26.509 29.051 51.305 55 .?53 59.342 63.691 66.?66 50 2?.991 29.?0? 32.35? 34.?64 3?.639 63.16? 6?.505 ?1.420 ?6.154 79.490 60 35.534 3?.435 40.432 43.133 46.459 ?4.39? ?9 .032 33.293 33.3?9 91.952 ?0 43.2?5 45.442 43.?53 51 .?39 55.329 35.52? 90.531 95.023 100.425 104.215 30 51.1?2 53.540 5?.153 60.391 64.2?3 96.5?3 101.3?9 106.629 112.329 116.321 90 59.196 61.?54 65.64? 69.126 ?3.291 10?.565 113.145 113.136 124.116 123.299 100 6?.323 ?0.065 ?4.222 ??.929 32.353 113.493 124.342 129.561 135.30? 140.169