For each of the following, find the P-value using Table C. Then calculate a more precise value using technology.

a. χ² = 19.03, df = 11

b. χ² = 19.03, df = 3

Table C

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Table C Chi-square distribution critical values Tail probability p df .25 .20 .15 .10 .05 .025 .02 .01 .005 .0025 .001 .0005 1 1.32 1.64 2.07 2.71 3.84 5.02 5.41 6.63 7.88 9.14 10.83 12.12 2 2.77 3.22 3.79 4.61 5.99 7.38 7.82 9.21 10.60 11.98 13.82 15.20 3 4.11 4.64 5.32 6.25 7.81 9.35 9.84 11.34 12.84 14.32 16.27 17.73 4 5.39 5.99 6.74 7.78 9.49 11.14 11.67 13.28 14.86 16.42 18.47 20.00 5 6.63 7.29 8.12 9.24 11.07 12.83 13.39 15.09 16.75 18.39 20.51 22.11 22.46 24.10 16.62 18.48 20.28 22.04 24.32 26.02 7.84 8.56 9.45 10.64 12.59 14.45 15.03 16.81 18.55 20.25 7 9.04 9.80 10.75 12.02 14.07 16.01 8 10.22 11.03 12.03 13.36 15.51 17.53 18.17 20.09 21.95 23.77 26.12 27.87 11.39 12.24 13.29 14.68 16.92 19.02 19.68 21.67 23.59 25.46 27.88 29.67 10 12.55 13.44 14.53 15.99 18.31 20.48 21.16 23.21 25.19 27.11 29.59 31.42 11 13.70 14.63 15.77 17.28 19.68 21.92 22.62 24.72 26.76 28.73 31.26 33.14 12 14.85 15.81 16.99 18.55 21.03 23.34 24.05 26.22 28.30 30.32 32.91 34.82 13 15.98 16.98 18.20 19.81 22.36 24.74 25.47 27.69 29.82 31.88 34.53 36.48 14 17.12 18.15 19.41 21.06 23.68 26.12 26.87 29.14 31.32 33.43 36.12 38.11 15 18.25 19.31 20.60 22.31 25.00 27.49 28.26 30.58 32.80 34.95 37.70 39.72 16 19.37 20.47 21.79 23.54 26.30 28.85 29.63 32.00 34.27 36.46 39.25 41.31 17 20.49 21.61 22.98 24.77 27.59 30.19 31.00 33.41 35.72 37.95 40.79 42.88 18 21.60 22.76 24.16 25.99 28.87 31.53 32.35 34.81 37.16 39.42 42.31 44.43 19 22.72 23.90 25.33 27.20 30.14 32.85 33.69 36.19 38.58 40.88 43.82 45.97 35.02 37.57 40.00 42.34 45.31 47.50 46.80 49.01 20 23.83 25.04 26.50 28.41 31.41 34.17 21 24.93 26.17 27.66 29.62 32.67 35.48 36.34 38.93 41.40 43.78 22 26.04 27.30 28.82 30.81 33.92 36.78 37.66 40.29 42.80 45.20 48.27 50.51 23 27.14 28.43 29.98 32.01 35.17 38.08 38.97 41.64 44.18 46.62 49.73 52.00 24 28.24 29.55 31.13 33.20 36.42 39.36 40.27 42.98 45.56 48.03 51.18 53.48 25 29.34 30.68 32.28 34.38 37.65 40.65 41.57 44.31 46.93 49.44 52.62 54.95 26 30.43 31.79 33.43 35.56 38.89 41.92 42.86 45.64 48.29 50.83 54.05 56.41 27 31.53 32.91 34.57 36.74 40.11 43.19 44.14 46.96 49.64 52.22 55.48 57.86 28 32.62 34.03 35.71 37.92 41.34 44.46 45.42 48.28 50.99 53.59 56.89 59.30 29 33.71 35.14 36.85 39.09 42.56 45.72 46.69 49.59 52.34 54.97 58.30 60.73 30 34.80 36.25 37.99 40.26 43.77 46.98 47.96 50.89 53.67 56.33 59.70 62.16 76.09 79.49 82.66 86.66 89.56 40 45.62 47.27 49.24 51.81 55.76 59.34 60.44 63.69 66.77 69.70 73.40 50 56.33 58.16 60.35 63.17 67.50 71.42 72.61 76.15 60 66.98 68.97 71.34 74.40 79.08 83.30 84.58 88.38 91.95 95.34 99.61 102.7 80 88.13 90.41 93.11 96.58 101.9 106.6 108.1 112.3 116.3 120.1 124.8 128.3 100 109.1 111.7 114.7 118.5 124.3 129.6 131.1 135.8 140.2 144.3 149.4 153.2