Nothing
## ---- include = FALSE---------------------------------------------------------
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>",
message = FALSE,
warning = FALSE
)
## -----------------------------------------------------------------------------
biology <- c(3, 7, 11, 0, 7, 0, 4, 5, 6, 2, 4, 7, 2, 9)
english <- c(8, 5, 4, 10, 4, 5, 7, 2, 6, 1, 2, 7, 0, 6, 4, 12, 5, 2)
qqnorm(biology)
qqline(biology)
## -----------------------------------------------------------------------------
qqnorm(english)
qqline(english)
## ---- echo = FALSE------------------------------------------------------------
got_ggplot2 <- requireNamespace("ggplot2", quietly = TRUE)
## ---- eval = got_ggplot2------------------------------------------------------
library(ggplot2)
# make a data frame in long format for plotting
test_results <- data.frame(
score = c(biology, english),
department = c(
rep("biology", length(biology)),
rep("english", length(english))
)
)
ggplot(test_results, aes(x = department, y = score, color = department)) +
geom_boxplot() +
geom_jitter() +
scale_color_brewer(type = "qual", palette = 2) +
theme_minimal() +
theme(legend.position = "none")
## -----------------------------------------------------------------------------
delta_0 <- 0
# by assumption
sigma_sq_1 <- 3
sigma_sq_2 <- 2
n_1 <- length(biology)
n_2 <- length(english)
# calculate the z-statistic
z_stat <- (mean(biology) - mean(english) - delta_0) /
sqrt(sigma_sq_1 / n_1 + sigma_sq_2 / n_2)
z_stat
## -----------------------------------------------------------------------------
library(distributions3)
Z <- Normal(0, 1) # make a standard normal r.v.
1 - cdf(Z, 0.376) + cdf(Z, -0.376)
## -----------------------------------------------------------------------------
1 - cdf(Z, abs(z_stat)) + cdf(Z, -abs(z_stat))
## -----------------------------------------------------------------------------
2 * cdf(Z, -0.376)
## -----------------------------------------------------------------------------
1 - cdf(Z, -0.376)
## -----------------------------------------------------------------------------
cdf(Z, -0.376)
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