<>= ## 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: \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} 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}