It is common knowledge that a fair coin lands heads up 50% of the time and tails up 50% of the time. For fair coins, a probability of 0 is assigned to the coin landing on its edge. But what if several coins were glued together? A teacher claims that if 10 pennies were glued together and flipped many times, the penny stack would land on heads 25% of the time, on tails 25% of the time, and on its edge 50% of the time. To investigate this claim, a student glues 10 pennies together and flips the stack 200 times. The student finds that the stack lands on heads 42 times, tails 41 times, and its edge 117 times. The student would like to know if there is convincing evidence that the distribution differs from what the teacher claimed. What is the value of the chi-square test statistic and P-value?Find the chi-square table here.χ2 = 5.79, P-value is between 0.05 and 0.10χ2 = 5.79, P-value is between 0.10 and 0.15χ2 = 5.97, P-value is between 0.025 and 0.05χ2 = 5.97, P-value is between 0.10 and 0.15 x² Critical ValuesProbability pdf.25.20.15.10.05.025.02.01.005 .0025 .001 .000511.321.642.072.713.845.025.416.637.889.1410.83 12.1222.773.223.794.615.997.387.829.2110.61 11.98 13.82 15.204.114.645.326.257.819.359.8411.34 12.84 14.32 16.27 17.7345.395.996.747.789.49 11.14 11.67 13.28 14.86 16.42 18.47 20.0056.637.298.129.2411.07 12.83 13.39 15.09 16.75 18.39 20.51 22.117.848.569.45 10.64 12.59 14.45 15.03 16.81 18.55 20.25 22.46 24.1079.049.8010.75 12.02 14.07 16.01 16.62 18.48 20.28 22.04 24.32 26.02810.22 11.03 12.03 13.36 15.51 17.53 18.17 20.09 21.95 23.77 26.12 27.87911.39 12.24 13.29 14.68 16.92 19.02 19.68 21.67 23.59 25.46 27.88 29.671012.55 13.44 14.53 15.99 18.31 20.48 21.16 23.21 25.19 27.11 29.59 31.421113.70 14.63 15.77 17.28 19.68 21.92 22.62 24.72 26.76 28.73 31.26 33.141214.85 15.81 16.99 18.55 21.03 23.34 24.05 26.22 28.30 30.32 32.91 34.821315.98 16.98 18.20 19.81 22.36 24.74 25.47 27.69 29.82 31.88 34.53 36.481417.12 18.15 19.41 21.06 23.68 26.12 26.87 29.14 31.32 33.43 36.12 38.111518.25 19.31 20.60 22.31 25.00 27.49 28.26 30.58 32.80 34.95 37.70 39.721619.37 20.47 21.79 23.54 26.30 28.85 29.63 32.00 34.27 36.46 39.25 41.311720.49 21.61 22.98 24.77 27.59 30.19 31.00 33.41 35.72 37.95 40.79 42.881821.60 22.76 24.16 25.99 28.87 31.53 32.35 34.81 37.16 39.42 42.31 44.431922.72 23.90 25.33 27.20 30.14 32.85 33.69 36.19 38.58 40.88 43.82 45.972023.83 25.04 26.50 28.41 31.41 34.17 35.02 37.57 40.00 42.34 45.31 47.502124.93 26.17 27.66 29.62 32.67 35.48 36.34 38.93 41.40 43.78 46.80 49.012226.04 27.30 28.82 30.81 33.92 36.78 37.66 40.29 42.80 45.20 48.27 50.512327.14 28.43 29.98 32.01 35.17 38.08 38.97 41.64 44.18 46.62 49.73 52.002428.24 29.55 31.13 33.20 36.42 39.36 40.27 42.98 45.56 48.03 51.18 53.482529.34 30.68 32.28 34.38 37.65 40.65 41.57 44.31 46.93 49.44 52.62 54.952630.43 31.79 33.43 35.56 38.89 41.92 42.86 45.64 48.29 50.83 54.05 56.412731.53 32.91 34.57 36.74 40.11 43.19 44.14 46.96 49.64 52.22 55.48 57.862832.62 34.03 35.71 37.92 41.34 44.46 45.42 48.28 50.99 53.59 56.89 59.302933.71 35.14 36.85 39.09 42.56 45.72 46.69 49.59 52.34 54.97 58.30 60.733034.80 36.25 37.99 40.26 43.77 46.98 47.96 50.89 53.67 56.33 59.70 62.164045.62 47.27 49.24 51.81 55.76 59.34 60.44 63.69 66.77 69.70 73.40 76.095056.33 58.16 60.35 63.17 67.50 71.42 72.61 76.15 79.49 82.66 86.66 89.566066.98 68.97 71.34 74.40 79.08 83.30 84.58 88.38 91.95 95.34 99.61 102.78088.13 90.41 93.11 96.58 101.9 106.6 108.1 112.3 116.3 120.1 124.8 128.3100109.1 111.7 114.7 118.5 124.3 129.6 131.1 135.8 140.2 144.3 149.4 153.2

The categorical variable is Penny stack. It has 3 categories which are heads, tails and edge. We have to test whether the distribution differs from what the teacher claimed or not. This is Chi-Square test for goodness-of-fit.Sample observed expected O - E (O - E)² / E Heads 42 200 (0.25) = 50.000 -8.000 1.280 Tails 41 200 (0.25) = 50.000 -9.000 1.620 Edge 117 200 (0.50) = 100.000 17.000 2.890 Total 200 200.000 0.000 5.79 The value of the test statistic is χ2= 5.79.Df = n-1 = 3-1 = 2 EXCEL command is “= CHIDIST (x, deg_freedom)” For p-value, enter in EXCEL as, “= CHIDIST (5.79, 2)” P-value = 0.0553. Correct Answer: χ2= 5.79, P-value is between 0.05 and 0.10.