Sampling and Experiments · Superchallenge problem

A population consists of six numbers: $1, 2, 3$ (stratum I) and $7, 8, 9$ (stratum II). Design A takes a simple random sample of 2 of the six numbers. Design B takes one number at random from each stratum. In each case $\bar{x}$ is the mean of the two numbers sampled. Find $\dfrac{\mathrm{Var}(\bar{x}) \text{ under A}}{\mathrm{Var}(\bar{x}) \text{ under B}}$.