CoCalc -- #6 homework.sagews

hw #6

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%r
1.
x<-c(1.23,1.33,.04,.44,1.2,.27,.48,.19,.83,.81,.71,.5,.49,1.16,.05,.15,.19,.77,1.08,.98,.63,.56,.41,.73,.34,.59,.34,.84,.5,.34,.28,.34,.87,.56,.17,.18,.19,.04,.49,1.1,.16,.1,.48,.21,.86,.52,.65,.27,.94,.4,.43,.25,.27)
mean(x)
sd(x)
1-pt(-10.98,52)

2.
prop.test(284,631,conf.level=.95)

3. 
x<-c(1.23,1.33,.04,.44,1.2,.27,.48,.19,.83,.81,.71,.5,.49,1.16,.05,.15,.19,.77,1.08,.98,.63,.56,.41,.73,.34,.59,.34,.84,.5,.34,.28,.34,.87,.56,.17,.18,.19,.04,.49,1.1,.16,.1,.48,.21,.86,.52,.65,.27,.94,.4,.43,.25,.27)

t.test(x,conf.level=.90)

4. 
x<-c(176,150,150,115,129,160,120,125,89,132,120,120,68,87,88,72,77,84,92,80,60,67,59,64,88,74,68)
t.test(x,cocnf.level=.95)

5. 
x<-c(45,51,39,41,48,49,46,43,47)
y<-c(171,178,157,163,172,183,173,175,173)
plot(x,y)

xbar = mean(x); ybar = mean(y);

SSxy = sum((x-xbar)*(y-ybar))
SSx = sum((x-xbar)^2)
b = SSxy/SSx
print(b)
a = ybar-b*xbar

sprintf("a = %2.2f", a); sprintf("b = %2.2f", b)

plot(x,y,col="blue",lwd=2)
lines(x,a+b*x,col="red")



6.
x<-c(45,51,39,41,48,49,46,43,47)
y<-c(171,178,157,163,172,183,173,175,173)

cor(x,y)
sprintf("coeff. of determination r^2=%2.4f",cor(x,y)^2)

0.527169811320755

0.341035625019815

0.999999999999998

	1-sample proportions test with continuity correction

data:  284 out of 631, null probability 0.5
X-squared = 6.0919, df = 1, p-value = 0.01358
alternative hypothesis: true p is not equal to 0.5
95 percent confidence interval:
 0.4108988 0.4898761
sample estimates:
        p 
0.4500792 

	One Sample t-test

data:  x
t = 11.254, df = 52, p-value = 1.506e-15
alternative hypothesis: true mean is not equal to 0
90 percent confidence interval:
 0.4487193 0.6056204
sample estimates:
mean of x 
0.5271698 

	One Sample t-test

data:  x
t = 15.563, df = 26, p-value = 1.085e-14
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
  87.24226 113.79478
sample estimates:
mean of x 
 100.5185 

[1] 1.69963

'a = 94.43'

'b = 1.70'

0.855968284268897

'coeff. of determination r^2=0.7327'