DA 22-23 seminar 22.R

#question 1
#a
alpha=5/100
sigma_sample=0.45/sqrt(25)
qnorm(alpha/2)
2.9-0.09*qnorm(0.025) #right boundary
2.9+0.09*qnorm(0.025) #left boundary

#b
(2.81-2.9)/(0.45/sqrt(25))
(2.99-2.9)/(0.45/sqrt(25))
pnorm(1)-pnorm(-1)

#question 2
0.01/2
qnorm(0.005)
0.12/sqrt(16)
4.07-0.03*(-2.575)
4.07+0.03*(-2.575)

#question 3
x<-c(18.2, 13.7,   15.9,   17.4,    21.8,  16.6,  12.3,	  18.8,	16.2)
mean(x)
qnorm(0.1/2)
16.76-3.8*(-1.64)/sqrt(9)
16.76+3.8*(-1.64)/sqrt(9)

#question 4
#a
20/100
qnorm(0.1)
187.9-32.4*qnorm(0.1)/sqrt(9)
187.9+32.4*qnorm(0.1)/sqrt(9)
#b
(210-187.9)/(32.4/sqrt(9))
(165.8-187.9)/(32.4/sqrt(9))
pnorm(2.04)-pnorm(-2.04)

#question 5
qnorm(0.025)
3.92+1.57/sqrt(1562)*(-1.96)
3.92-1.57/sqrt(1562)*(-1.96)

#question 6
qnorm(0.05)
3.81+(-1.6448)*1.34/sqrt(541)
3.81-(-1.6448)*1.34/sqrt(541)

#question 7
qnorm(0.05)
60.41+(-1.6448)*11.28/sqrt(352)
60.41-(-1.6448)*11.28/sqrt(352)

#question 8
(6.16-6.06)/(1.43/sqrt(174))
(5.96-6.06)/(1.43/sqrt(174))

pnorm(0.92)-pnorm(-0.92)

#question 9
qt(0.025,8)

157.82+(-2.306)*38.89/sqrt(9)
157.82-(-2.306)*38.89/sqrt(9)

#question 10
x<-c(18.2,  25.9,   6.3,  11.8,  15.4,   20.3,   16.8,  19.5,  12.3,   17.2)
mean(x)
sqrt(var(x))
qt(0.005,9)
16.37+(-3.249)*5.37/sqrt(10)
16.37-(-3.249)*5.37/sqrt(10)