✔ 最佳答案
擲一骰子120次.求在α=0.05下檢定.點數出現是否為均勻分配?Ans:均勻分配(Uniform Distribution)a=min=10, b=max=30f(x)=0......x<a, x>bf(x)={10次(6點) 15次(4點) 20次(2點) 20次(5點) 25次(4點) 30次(1點)}=1/(b-a)=1/(30-10)=1/20=0.05E(x)=(a+b)/2=(10+30)/2=40/2=20V(x)=(b-a)^2/12=(30-10)^2/12=20^2/12=400/12=100/3=33.3333xbar=(30+20+25+15+20+10)/6=120/6=20=E(x)v=自由度=4查表X^2(v=4,0.05)=11.0703
Ho: f(x)=1/xbarH1: f(x)=/=1/xbar
x^2=Σ(x-xbar)^2/xbar=Σ(x^2-2*xbar*x+xbar^2)/xbar=Σx^2/xbar-2Σx+Σxbar=Σx^2/xbar-2*N*Σx/N+xbarΣ1=Σx^2/xbar-2*N*xbar+N*xbar=Σx^2/xbar-N*xbar=(900+400+625+225+400+100)/20-6*20=132.5-120=12.5 > 11.0703=> 差異很大所以拒絕Ho