I am wondering what type of statistical test would be appropriate to test for a difference in means between two groups for which each measurement has a different uncertainty. For example, I want to see if there is a significant difference in height when comparing men and women, but each person was measured using a different type of ruler (let's say one ruler only measures up to a precision of 1 cm, another to 1 mm, etc). So, I would have a set of measurements like:

m = [170 cm, 150 cm, 200 cm]

w = [150 cm, 120 cm, 170 cm]

u_m = [1 cm, 0.5 cm, 0.1 cm]

u_w = [0.1 cm, 0.25 cm, 1 cm]

where order is preserved (i.e., u_m[1] is the uncertainty of m[1]).

What type of test could tell me if there is a significant difference in means (outputting a significance value) with the associated uncertainties taken into account?