#install.packages("DAAG")
library(DAAG)

data <- pair65
y <- pair65$heated - pair65$ambient

# test for the mean equal zero

help("t.test")
t.test(y)


# null distribution

n <- length(y)
curve(dt(x, 8), xlim=c(-6,6))
t_obs <- mean(y)/sqrt(var(y)/n)

# fixed level of significance

alpha <- 0.05
q.t.1 <- qt(alpha/2, 8)
q.t.2 <- qt(1-alpha/2,8)

segments(q.t.1, -0.1, q.t.1, dt(q.t.1,8), col ="red")
segments(q.t.2, -0.1, q.t.2, dt(q.t.2,8), col ="red")

t_obs
segments(t_obs, -0.1, t_obs, dt(t_obs,8), col ="blue")

# p-value

p_value <- 2*(1-pt(t_obs, n-1))


# temptative to make independent samples comparison

x1 <- pair65$heated
x2 <- pair65$ambient
t.test(x1, x2, var.equal = TRUE)


# t.test wit alpha = 0.001

t.test(y, conf.level = 0.99)

# wilcoxon rank test

wilcox.test(y)