I am conducting an experiment where I will measure the strength of a material used for roads. Ideally, I would like to use a large surface area to measure this but this takes too long and is really expensive. I therefore will scale it down to one area which is $50cm^2$ and one which is $12cm^2$. I then want to compare the data I get from both these samples and see how (if) they differ. For the smaller sample, I'll also be doing less observations, i.e I'll get around 30 values for the $50cm^2$ one and only like 3 or 4 for the $12cm^2$ due to how much it costs.
I was going to use the Normal Distribution, but as I won't have a lot of data, I can't justify using the Normal Distribution through the Central Limit Theorem.
Would I be able to use a non-parametric test like the Sign test? Or, would it actually be something like the Wilcoxon signed rank test as the data is paired isn't it? How would I compare the data from there?