WeBWorK Standalone Renderer

Greater Numbsville is comprised of three villages: Lower Numbsville (LN, residents), Old Numbsville (ON, residents), and Upper Numbsville (UN, residents). A crazed statistician decides to do the following survey to estimate the average age of Greater Numbsville residents. First he will flip a fair coin. If the coin comes up heads he will obtain a simple random sample of six Greater Numbsville residents. If the coin comes up tails he will instead do a stratified sample of Greater Numbsville residents, using the three villages as strata, with sample sizes of two for each stratum. He carries out his scheme and reports the following data on the sampled residents.

$\begin{array}{c|c} \text{village} & \text{age} \\ \hline \text{LN} & 39 \\ \text{LN} & 17 \\ \text{ON} & 36 \\ \text{ON} & 45 \\ \text{UN} & 65 \\ \text{UN} & 26 \end{array}$

To make your life difficult, however, the crazed statistician does not report the outcome of the coin toss. Outsmart the crazed statistician by using an unbiased procedure to report an estimate of the average age of Greater Numbsville residents nonetheless. (HINT: use sampling weights.) Report your answer to the nearest year.