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An example question with a multiple choice question.
<<echo=FALSE, results=hide>>=
## DATA GENERATION
mean.val<-round(rnorm(1,mean=100,sd=10),digits=0)
sd.val<-round(abs(rnorm(1,mean=10,sd=10)),digits=0)
n<-round(abs(rnorm(1,mean=100,sd=10)),digits=0)+1
se1<-round(sd.val/sqrt(n),digits=3)
se2<-round(sd.val/sqrt(n^2),digits=3)
questions <- character(5)
solutions <- logical(5)
explanations <- character(5)
questions[1] <- paste(se1,se2, sep = ",")
newse1<-2.1*se1
newse2<-13*se2
questions[2] <- paste(newse1,newse2,sep = ",")
newse1<-.5*se1
newse2<-se2
questions[3] <- paste(newse1,newse2, sep = ", ")
newse1<-se1
newse2<-.5*se2
questions[4] <- paste(newse1,newse2, sep = ", ")
newse1<-se1/2
newse2<-2*se2
questions[5] <- paste(newse1,newse2,sep = ", ")
solutions[1] <- T
solutions[2:5] <- F
explanations[1] <- "Apply the formula for standard error"
explanations[2:5] <- "See explanation"
@
\begin{question}
Suppose we sample from a population with a normal distribution and mean \Sexpr{mean.val} and standard deviation \Sexpr{sd.val}.
Sample size is \Sexpr{n}.
What is the standard error going to be when sample size is \Sexpr{n}, and what would it be when \Sexpr{n^2}?
\begin{answerlist}
\item \Sexpr{questions[1]}
\item \Sexpr{questions[2]}
\item \Sexpr{questions[3]}
\item \Sexpr{questions[4]}
\item \Sexpr{questions[5]}
\end{answerlist}
\end{question}
\begin{solution}
Always start with what you know. We know the mean and standard deviation. We can therefore compute exact standard errors, with the formula:
\begin{equation}
\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
\end{equation}
Now, if I increase the sample size, it's obvious that we have to simply re-calculate with a new $n$.
\begin{answerlist}
\item \Sexpr{mchoice2text(solutions[1])}. \Sexpr{explanations[1]}
\item \Sexpr{mchoice2text(solutions[2])}. \Sexpr{explanations[2]}
\item \Sexpr{mchoice2text(solutions[3])}. \Sexpr{explanations[3]}
\item \Sexpr{mchoice2text(solutions[4])}. \Sexpr{explanations[4]}
\item \Sexpr{mchoice2text(solutions[5])}. \Sexpr{explanations[5]}
\end{answerlist}
\end{solution}
%% META-INFORMATION
%% \extype{schoice}
%% \exsolution{\Sexpr{mchoice2string(solutions)}}
%% \exname{sesamplesize1}
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