# Exercice 1 v=c(2.4, 3.2,3.6,4.1,4.3,4.7,5.4,5.9,6.5,6.9) mean(v) var(v) t.test(v,conf.level = 0.95)$conf.int ## CI qu=quantile(replicate(10000, var(sample(v, replace=TRUE))), probs=c(0.025, 0.975)) sqrt(qu) # Exercice 2 library(SDMTools) CH=c(1170, 1220, 1270, 1320, 1370, 1420, 1470) nH=c(5, 36, 45, 50, 61, 49, 17) ntotal=sum(nH) moyenne=wt.mean(x=CH,wt=nH) moyenne stddev=wt.sd(x=CH,wt=nH) stddev E=qt(c(0.025,0.975),df=ntotal-1)*stddev/sqrt(ntotal) CI=moyenne+E CI #Exercice 3 hau=c(36, 37, 38, 39, 40, 41) nsoja=c(6,11,26,32,14,11) qusoja=quantile(replicate(100000, wt.var(x=sample(hau, replace=TRUE),wt=nsoja)), probs=c(0.025, 0.975)) qusoja # exercice 4 binom.test(x=330,n=400,conf.level=0.95)$conf.int binom.test(x=330,n=400,conf.level=0.99)$conf.int # exercice 5 binom.test(x=44,n=200,p=0.15,conf.level=0.95) # exercice 6 succes=c(6,15) essai=c(40,60) prop.test(succes,essai,alternative="two.sided") Ta=matrix(c(6, 34, 15, 45),nrow = 2) fisher.test(Ta) #exercice 7 E=qt(c(0.025,0.975),df=100-1)*0.4/sqrt(100) CI=2.6+E CI #exercice 8 a2=c(0.184,0.193,0.197,0.198,0.199,0.199,0.206,0.216,0.403) a3=c(0.354,0.359,0.361,0.362,0.364,0.373,0.382,0.258,0.413) var.test(a2,a3) t.test(a2,a3,var.equal =TRUE) # exercice 9 M1=c(2132,2275,2374,2400,2437,2402,2822,2892,2780,2833,2714,2705,2850,2799,2849,2742) M2=c(2678,2823,2713,2786,2700,2831,2823,2779,2766,2773,2828,2769,2836,2715,2846,2708) var.test(M1,M2) t.test(M1,M2,var.equal =FALSE) #exercice 10 FV=c(65,80,89,64,68,68,86,54,91,77) PF=c(53,63,90,52,64,50,88,35,102,59) t.test(FV,PF,paired=T) #exercice 11 espA=c(242,253,271,292,305,332,335,337,338,350,357,364,365,371,372,385,401, 402,410,412,418,423,427) espB=c(202,203,208,233,251,258,271,282,283,301,308,314,327) result1=wilcox.test(espA, espB, paired = F, alternative = "two.sided") #test bilatéral result1 #exercice 12 NM=c(9.2,10,9,9.4,10.1,9.5,10,10.3,10.2,10.2,9.8,10.1) #nouvelle methode MR=c(9.5,9,8.8,9.5,9.1,10,10.1,9.3,9,9.7,9.1,9.3) #methode de reference result2=wilcox.test(NM, MR, paired = T, alternative = "two.sided") #test apparie result2 # exercice 13 note=c(71,67,55,64,82,66,74,58,79,61,78,46,84,93,72,54,78,86,48,52) result3=wilcox.test(note, mu=66, alternative = "two.sided") result3 result4=wilcox.test(note, mu=75, alternative = "two.sided") result4 # exercice 14 fx=c(12,15,18,22,3,7,4,17,20) fy=c(14,7,20,18,8,3,6,12,19) rs=cor.test(fx,fy,method="spearman") rs # Exercice 15 e1=c(3,9.8,2,5.2,3.6,5.9,8.5,9.4) e2=c(9.3,12.5,11.3,7.6,3.2,8.6,7.2,14.2,9.6,3.2) result5=wilcox.test(e1, e2, paired = F, alternative = "two.sided") result5 # Exercice 16 silice=c(6,4,12,1,10,5,8,2,11,7,3,9) fer=c(3,9,11,2,12,4,10,5,8,1,6,7) rs2=cor.test(silice,fer,method="spearman") rs2 # Exercice 17 ob=c(29,19,18,25,17,10,15,11) result6=chisq.test(ob) # test le vecteur contre l'hypothese d'equiprobabilité result6 # avec le chi-2 # Exercice 18 TN=c(16.2,30.5,16.9,16.0,40.2,38.4,41.3,43.9,28.3,33.9,44.2) TU=c(55.0,27.3,33.3,56.5,11.5,14.2,13.9,19.0,33.1,43.2,28.5) plot(TU,TN) fit=lm(TN~TU) summary(fit) abline(fit$coefficients[1],fit$coefficients[2],col="blue") # Exercice 19 X=c(-2,-1,0,1,2) Y=c(131,113,89,51,7) fit2=lm(Y~X + I(X^2)) fit2 # Exercice 20 XA=c(10,20,30,40,50,60) YA=c(409,304,260,192,170,150) dat=as.data.frame(cbind(XA,YA)) modele <- nls(YA~V0*exp(lambda*XA),data=dat,start=list(V0=600,lambda=-0.1)) #Exercice 21 fr <- data.frame(var = c(8,9,9,6,9,10,9,10,10,9,12,11,6,8,8,7),categ = factor(c(rep("A",4),rep("B",4),rep("C",4),rep("D",4)))) res <- bartlett.test(var ~ categ, fr) res tes <- oneway.test(var ~ categ, fr, var.equal = TRUE) tes #ou fit <- aov(var ~ categ, fr) summary(fit) TukeyHSD(fit)