In exams: Automatic Generation of Exams in R

#| include: false
s <- sample(levels(penguins$species), 1)

Question

The penguins data in base R provides various measurements of adult penguins from three different species. See ?penguins for more details. Originally, the data was used to study sex dimorphism separately for the three species.

The first three rows of the data can be inspected as follows. Employ summary() to obtain a first overview.

data("penguins", package = "datasets")
head(penguins, 3)

Explore the sex differences with respect to body mass (weight, in grams) of the penguins. Create parallel boxplots of weight by sex, such as the one below, separately for the three species.

#| echo: false
#| fig-height: 5
#| fig-width: 5
#| fig-cap: ""
p <- penguins[penguins$species == s, ]
plot(body_mass ~ sex, data = p)

Which species does this plot pertain to? r add_cloze(s)

To complement the plot complete the corresponding table of groupwise statistics:

#| echo: false
tab <- aggregate(body_mass ~ sex, data = p,
  FUN = function(x) c(median = median(x), mean = mean(x), `std. deviation` = sd(x)))
rownames(tab$body_mass) <- tab$sex
tab <- as.data.frame(tab$body_mass)

r add_cloze(tab, tolerance = 0.1)

The average weight difference of r add_cloze(diff(tab$mean), tolerance = 0.1) is thus slightly r add_cloze("higher", c("lower", "higher")) than the median weight difference of r add_cloze(diff(tab$median), tolerance = 0.1).

Compute the full summary() of weight by sex for this species and select the correct statements in the following list.

#| echo: false
tab2 <- aggregate(body_mass ~ sex, data = p, FUN = summary)$body_mass
ans <- character(3)
sol <- logical(3)

ans[1] <- "The standard deviation of weight is lower for males compared to females."
sol[1] <- tab[2,3] < tab[1,3]

ans[2] <- sprintf("None of the penguins weighs less than %s grams.", min(tab2[,1]))
sol[2] <- all(p$body_mass >= min(tab2[,1]), na.rm = TRUE)

sx <- sample(1:2, 1)
sol[3] <- sample(c(TRUE, FALSE), 1)
ans[3] <- sprintf("Less than half of the %s penguins weigh more than %s grams.",
  levels(p$sex)[sx], if (sol[3]) tab2[sx, 5] else tab2[sx, 2])

r add_cloze(setNames(sol, ans), type = "mchoice")

r format_metainfo("answerlist")

Solution

One way to obtain the exploratory boxplots separately for the three species is:

#| fig-height: 4.5
#| fig-width: 13.5
#| fig-cap: ""
par(mfrow = c(1, 3))
for(i in levels(penguins$species)) plot(body_mass ~ sex, data = penguins,
  subset = species == i, main = i, ylim = range(penguins$body_mass, na.rm = TRUE))

The question shows the parallel boxplots for the r s species.

Groupwise statistics of body mass by sex and species (including mean, median, and standard deviation) can be obtained by aggregating the data with the combined summary() and sd() functions.

aggregate(body_mass ~ sex + species, data = penguins,
  FUN = function(x) c(summary(x), `Std. dev.` = sd(x)))

Based on this the remaining elements of the question can be answered.

Metainformation

exname: penguins sex dimorphism extype: cloze exclozetype: r format_metainfo("type") exsolution: r format_metainfo("solution") extol: r format_metainfo("tolerance") exshuffle: TRUE