One Sample t-test
data: observations
t = 0.41662, df = 12, p-value = 0.6843
alternative hypothesis: true mean is not equal to 18
99 percent confidence interval:
16.80671 19.57021
sample estimates:
mean of x
18.18846
Last active
February 19, 2022 21:05
-
-
Save TeWu/60ca98e9dff514023d3276eb6706702d to your computer and use it in GitHub Desktop.
R Student's t-Test
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
observations <- c(17.13, 17.71, 17.51, 19.39, 17.70, 19.15, 17.17, 18.48, 21.71, 19.55, 17.63, 18.55, 14.77) | |
tr <- t.test(observations, mu=18, conf.level=0.99) | |
tr # print Test Results | |
# Plot t-distribution | |
stderr <- sqrt(var(observations)/length(observations)) | |
x <- seq(-4, 4, by=0.01) | |
y <- dt(x, df=tr$parameter) | |
plot(x, y, type='l') | |
abline(v=0, col="black") | |
abline(v=tr$statistic, col="blue") # t-statistic | |
abline(v=(tr$conf.int[1:2] - tr$null.value) / stderr, col="red") # confidance interval | |
# Plot normal distribution approximation | |
x <- seq(tr$estimate - 4 * stderr, tr$estimate + 4 * stderr, by=0.1) | |
y <- dnorm(x, mean=tr$estimate, sd=stderr) | |
plot(x, y, type='l', col="blue") | |
# polygon(c(min(x), x[x<tr$conf.int[1]], tr$conf.int[1], tr$conf.int[1]), | |
# c(0, y[x<tr$conf.int[1]], dnorm(tr$conf.int[1], mean=tr$estimate, sd=stderr), 0), | |
# col="pink") | |
# polygon(c(tr$conf.int[2], x[x>tr$conf.int[2]], max(x), tr$conf.int[2]), | |
# c(dnorm(tr$conf.int[2], mean=tr$estimate, sd=stderr), y[x>tr$conf.int[2]], 0, 0), | |
# col="pink") | |
abline(v=tr$null.value, col="black") # H0 mean | |
abline(v=tr$estimate, col="blue") # estimated mean | |
abline(v=tr$conf.int[1:2], col="red") # confidance interval - there is 99% probability the true mean is inside this interval |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment