Andrew Sommese 2005with(plots):

Warning, the name changecoords has been redefined

n[0]:=185;n[1]:=1149; n[2]:= 3265;n[3]:=5475; n[4]:= 6114; n[5]:= 5194;n[6]:= 3067; n[7]:= 1331; n[8]:= 403;n[9]:=105; n[10]:= 14; n[11]:= 4; n[12]:= 0;

NiM+Jkkibkc2IjYjIiIhIiQmPQ==NiM+Jkkibkc2IjYjIiIiIiVcNg==NiM+Jkkibkc2IjYjIiIjIiVsSw==NiM+Jkkibkc2IjYjIiIkIiV2YQ==NiM+Jkkibkc2IjYjIiIlIiU5aA==NiM+Jkkibkc2IjYjIiImIiUlPiY=NiM+Jkkibkc2IjYjIiInIiVuSQ==NiM+Jkkibkc2IjYjIiIoIiVKOA==NiM+Jkkibkc2IjYjIiIpIiQuJQ==NiM+Jkkibkc2IjYjIiIqIiQwIg==NiM+Jkkibkc2IjYjIiM1IiM5NiM+Jkkibkc2IjYjIiM2IiIlNiM+Jkkibkc2IjYjIiM3IiIh

sum(n[k],k=0..12);

NiMiJjFqIw==

for m from 0 to 12 do k[m]:= evalf(26306*binomial(12,m)*(1/3)^m*(2/3)^(12-m)); od;

NiM+Jkkia0c2IjYjIiIhJCIrL1lcRj8hIig=NiM+Jkkia0c2IjYjIiIiJCIram5cOzchIic=NiM+Jkkia0c2IjYjIiIjJCIrKDRtYE0kISInNiM+Jkkia0c2IjYjIiIkJCIraSxodmIhIic=NiM+Jkkia0c2IjYjIiIlJCIrSzljc2khIic=NiM+Jkkia0c2IjYjIiImJCIrWSJcIT1dISInNiM+Jkkia0c2IjYjIiInJCIrTmA+RkghIic=NiM+Jkkia0c2IjYjIiIoJCIrJ0c3WEQiISInNiM+Jkkia0c2IjYjIiIpJCIrJiozTj9SISIoNiM+Jkkia0c2IjYjIiIqJCIreTMqPXIpISIpNiM+Jkkia0c2IjYjIiM1JCIrS095MTghIik=NiM+Jkkia0c2IjYjIiM2JCIrP14pej0iISIqNiM+Jkkia0c2IjYjIiM3JCIrKip6JCpcXCEjNg==

chi-square analysischisquare12:=sum((k[j]-n[j])^2/(k[j]),j=0..12);

NiM+SSxjaGlzcXVhcmUxMkc2IiQiKypHQTc4JSEiKQ==

1-stats[statevalf,cdf,chisquare[12]](chisquare12);

NiMkIicnW00lISM1

so 0% of similar data samples from the expected distribution would have a larger chi-square statistic.A:=listplot([seq([j,n[j]],j=0..12)]):B:= listplot([seq([j,k[j]],j=0..10)]):display({A,B});

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

the 7006 reliable experimentsnR[0]:=45;nR[1]:=327; nR[2]:= 886;nR[3]:=1475; nR[4]:= 1571; nR[5]:= 1404;nR[6]:= 787; nR[7]:= 367; nR[8]:= 112;nR[9]:=29; nR[10]:= 2; nR[11]:= 1; nR[12]:= 0;

NiM+JkkjblJHNiI2IyIiISIjWA==NiM+JkkjblJHNiI2IyIiIiIkRiQ=NiM+JkkjblJHNiI2IyIiIyIkJykpNiM+JkkjblJHNiI2IyIiJCIldjk=NiM+JkkjblJHNiI2IyIiJSIlcjo=NiM+JkkjblJHNiI2IyIiJiIlLzk=NiM+JkkjblJHNiI2IyIiJyIkKHk=NiM+JkkjblJHNiI2IyIiKCIkbiQ=NiM+JkkjblJHNiI2IyIiKSIkNyI=NiM+JkkjblJHNiI2IyIiKiIjSA==NiM+JkkjblJHNiI2IyIjNSIiIw==NiM+JkkjblJHNiI2IyIjNiIiIg==NiM+JkkjblJHNiI2IyIjNyIiIQ==

sum(nR[k],k=0..12);

NiMiJTFx

for m from 0 to 12 do k[m]:= evalf(7006*binomial(12,m)*(1/3)^m*(2/3)^(12-m)); od;

NiM+Jkkia0c2IjYjIiIhJCIrW3F3KlImISIpNiM+Jkkia0c2IjYjIiIiJCIrSC0nKVJLISIoNiM+Jkkia0c2IjYjIiIjJCIrSWNoNCopISIoNiM+Jkkia0c2IjYjIiIkJCIrUWYkXFsiISInNiM+Jkkia0c2IjYjIiIlJCIrSkhicTshIic=NiM+Jkkia0c2IjYjIiImJCIrV0JXTzghIic=NiM+Jkkia0c2IjYjIiInJCIrd08iZnooISIoNiM+Jkkia0c2IjYjIiIoJCIraGU1VEwhIig=NiM+Jkkia0c2IjYjIiIpJCIrI2UmNFc1ISIoNiM+Jkkia0c2IjYjIiIqJCIrL0NAP0IhIik=NiM+Jkkia0c2IjYjIiM1JCIrMCc9LlskISIqNiM+Jkkia0c2IjYjIiM2JCIrMGcjUjskISM1NiM+Jkkia0c2IjYjIiM3JCIrLURJPTghIzY=

chi-square analysischisquare12:=sum((k[j]-nR[j])^2/(k[j]),j=0..12);

NiM+SSxjaGlzcXVhcmUxMkc2IiQiKyZbZyhSPSEiKQ==

1-stats[statevalf,cdf,chisquare[12]](chisquare12);

NiMkIitgUlNUNSEjNQ==

so 0% of similar data samples from the expected distribution would have a larger chi-square statistic.A:=listplot([seq([j,nR[j]],j=0..12)]):B:= listplot([seq([j,k[j]],j=0..10)]):display({A,B});

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

the 26306 experiments minus the 7006 reliable experimentsfor j from 0 to 12 do nU[j]:=n[j]-nR[j];od;

NiM+JkkjblVHNiI2IyIiISIkUyI=NiM+JkkjblVHNiI2IyIiIiIkQSk=NiM+JkkjblVHNiI2IyIiIyIlekI=NiM+JkkjblVHNiI2IyIiJCIlK1M=NiM+JkkjblVHNiI2IyIiJSIlVlg=NiM+JkkjblVHNiI2IyIiJiIlIXokNiM+JkkjblVHNiI2IyIiJyIlIUcjNiM+JkkjblVHNiI2IyIiKCIkayo=NiM+JkkjblVHNiI2IyIiKSIkIkg=NiM+JkkjblVHNiI2IyIiKiIjdw==NiM+JkkjblVHNiI2IyIjNSIjNw==NiM+JkkjblVHNiI2IyIjNiIiJA==NiM+JkkjblVHNiI2IyIjNyIiIQ==

sum(nU[k],k=0..12);

NiMiJiskPg==

for m from 0 to 12 do k[m]:= evalf((26306-7006)*binomial(12,m)*(1/3)^m*(2/3)^(12-m)); od;

NiM+Jkkia0c2IjYjIiIhJCIrKip5XihbIiEiKA==NiM+Jkkia0c2IjYjIiIiJCIrKFIyXiMqKSEiKA==NiM+Jkkia0c2IjYjIiIjJCIrTVhTYUMhIic=NiM+Jkkia0c2IjYjIiIkJCIrQlVuITQlISInNiM+Jkkia0c2IjYjIiIlJCIrLCYzP2clISInNiM+Jkkia0c2IjYjIiImJCIrLG9nIm8kISInNiM+Jkkia0c2IjYjIiInJCIrblJnWkAhIic=NiM+Jkkia0c2IjYjIiIoJCIrLnEsLyMqISIoNiM+Jkkia0c2IjYjIiIpJCIrOGBEd0chIig=NiM+Jkkia0c2IjYjIiIqJCIrdSV5O1InISIpNiM+Jkkia0c2IjYjIiM1JCIrNnheKGUqISIqNiM+Jkkia0c2IjYjIiM2JCIrIz5EZnIpISM1NiM+Jkkia0c2IjYjIiM3JCIrKFxOO2okISM2

chi-square analysism:='m';chisquare12:=sum((k[m]-nU[m])^2/(k[m]),m=0..12);

NiM+SSJtRzYiRiQ=NiM+SSxjaGlzcXVhcmUxMkc2IiQiK0YmeV5GJCEiKQ==

1-stats[statevalf,cdf,chisquare[12]](chisquare12);

NiMkIikvPmU1ISM1

so 0% of similar data samples from the expected distribution would have a larger chi-square statistic.A:=listplot([seq([j,nU[j]],j=0..12)]):B:= listplot([seq([j,k[j]],j=0..10)]):display({A,B});

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