m <- 139.13
c <- 142
sigma <- sqrt(39.112)
n <- 15
alpha <- 0.05


t0 <- (m-c)/(sigma/sqrt(n))
t0

qnorm(alpha)

HH <- m-sigma/sqrt(n)*qnorm(alpha)
HH

pnorm(t0)



X <- c(10.24, 10.12, 9.91, 10.19, 9.78, 10.14, 9.86, 10.17, 10.05)
sum(X)
m <- mean(X)
s <- sd(X)
c <- 10

n <- length(X)
alpha <- 0.05

t0 <- (m-c)/(s/sqrt(n))
t0

qt(alpha/2, n-1)
qt(1-alpha/2, n-1)

2*min(pt(t0, n-1), 1-pt(t0, n-1))

n <- 25
s <- 0.1
alpha <- 0.05



dh <- (n-1)*s^2/qchisq(1-alpha/2, n-1)
hh <- (n-1)*s^2/qchisq(alpha/2, n-1)

dh
hh

sqrt(dh)
sqrt(hh)

X <- c(1.8, 1.0, 2.2, 0.9, 1.5, 1.6)
Y <- c(1.5, 1.1, 2.0, 1.1, 1.4, 1.4)


Z <- X-Y
Z

m <- mean(Z)
s <- sd(Z)
c <- 0
n <- 6
alpha <- 0.05

t0 <- (m-c)/(s/sqrt(n))
t0

qt(alpha/2, n-1)
qt(1-alpha/2, n-1)

2*min(pt(t0, n-1), 1-pt(t0, n-1))