In personality research, it is well documented that women are more anxious than men. (On average. Overlapping Bell curves, yadda yadda, d~0.4 or so.) This probably isn't surprising to you, since the effect is big enough that it should be noticeable in your personal life.

I think people commonly interpret this fact as meaning that women are higher in what I'd call the "general factor of anxiety" than men. That is, across a wide variety of unrelated situations, women would find things more worrying than men.

However, personality measures of anxiety are not really designed to measure the general factor of anxiety. Instead e.g. 

 's Anxiety scale just asks questions roughly synonymous with "How anxious are you?" over and over again.

There are some cases where it would seem like women face anxiety-worthy things that men don't face as much. For instance women are surrounded by people who are much bigger and stronger than them and could totally beat them in a fight. And women face certain sorts of gender norms that men don't have (though men may face other gender norms so YMMV), e.g. women may be judged more than men by how good they look or how messy their home is. These sorts of factors could cause women to 

 be worried about these problems while not necessarily being extra worried about random things more generally.

This could probably be assessed in many ways, but one way that will be considered sufficient for this question is using standard survey methods. It should be possible to design an anxiety test that asks about 

 kinds of anxiety (e.g. "Do you feel afraid of big angry-looking men with tattoos?"). If someone designs a test like this which mainly focuses on factors where neither men nor women have special reasons to be anxious (such that it would presumably assess sex differences in general anxiety), and finds that the sex difference on the general factor of society is at least 75% of the overall sex difference in anxiety (as measured by Cohen's d), this question resolves YES. If they find it to be less than 75% of the overall sex difference in anxiety, this question resolves NO.

The question might also resolve based on other things, but I consider it unlikely. The question will not resolve based on some galaxybrained indirect strategy. I will likely run the study described in the resolution criteria at some point.