my_sample <- c(80, 90, 100, 80, 130)
mu0 <- 125
mean(my_sample)
t.test(my_sample, mu = mu0, alternative = 'greater')
# mu > mu0
curve(dt(x, df=4), from = -5, to=5)
# exercise
# Find p-value for alternative = 'less'
# We can do it without R
1 - 0.9824
t.test(my_sample, mu = mu0, alternative = 'less')
# Find p-value for alternative = 'two.sided'
# H1: mu != mu0
# We do it without R
t.test(my_sample, mu = mu0, alternative = 'two.sided')
0.01764 * 2
x <- c(3, 2, 5, 1, 7) # treatment group
y <- c(4, 5, 3, 5, 7, 8) # control group
t.test(x, y, alternative = 'less')
t.test(x, y, alternative = 'two.sided')
t.test(rep(x, 3), rep(y, 3), alternative = 'less')
dat <- read.csv("https://bit.ly/39Fr0gD")
# Is it true that time for round sounds is
# greater or less than time for unrounded sounds?
round_times <- dat[dat$roundness == "round", "time"]
# get values of time variable
# where roundness == "round"
dat[dat$roundness == "round", "time"]

unrounded_times <- dat[dat$roundness == "unrounded", "time"]
round_times
mean(round_times)
sd(round_times)
length(round_times)

mean(unrounded_times)
sd(unrounded_times)
length(unrounded_times)

# Exercise:
# use t.test to test a hypothesis
# and answer: can we say that
# there is a statistically significant
# difference between round and unrounded times?

t.test(round_times, unrounded_times)
# p-value = 0.33 > 0.05 => do not reject H0

t.test(time ~ roundness, data=dat)
unique(dat$roundness)

t.test(vowel.dur ~ roundness, data=dat)