I'm tempted to agree with DragonGod on a weaker form (or phrasing) of the "I exist" proposition:
I would defend the proposition that my feeling of subjective experience (independent of whether or not I am mistaken about literally everything I think and believe) really does exist with a probability of 1. And even if my entire experience was just a dream or simulated on some computer inside a universe where 2+2=3 actually holds true, the existence of my subjective experience (as opposed to whatever "I" might mean) seems beyond any possible doubt.
Even if every single one of my senses and my entire map of reality (even including the concept of reality itself) was entirely mistaken in every possible aspect, there would still be such a thing as having/being my subjective experience. It's the one and only true axiom in this world that I think we can assign P=1 to.
Especially if you don't conceive of the word "exist" as meaning "is a thing within the base level of reality as opposed to a simulation."
Background: My wife and I are both studying psychology, I'm doing my M.Sc. she does a very similar study on health risks at the workplace (an adaptive one, if general questions are answered "unfavorably" (i.e. indicator a health risk at the workplace is present), then a handful of more in-depth related questions to pinpoint the exact problem are given.
I didn't take the test yet, but just by reading ChristianKI's objections/suggestions (with which I agree) you need to really clarify the questions.
Here's a helpful piece of advice I've been given: Don't think about if the question is understandable, ask yourself if there is any chance at all that it could possibly be misunderstood by someone somewhere and change it as often as you need until that is no longer the case.
With your cancer event - how could you be sure that the partner would not want to talk about it or be involved in the situation?
She was under a lot of stress due to an ungodly amount of near simultaneous university exams and under high pressure of failing her course if she didn't ace all of them (luckily she pulled through). She had also lost her father to cancer about a year before this event and was still suffering the effects. In fact, with the death of her father she had lost both her parents and next to her brother I'm her "only real family" and we had been together for about five years at that point.
My prediction of how she would have reacted to the possibility of me having cancer was that she would not have been able to focus on her studies and exams very well, possibly fail an education she had invested years of her life and a huge sum of money into and generally have an unbelievably miserable time during the weeks until anything conclusive about the lump would have been found. I on the other hand was actually fairly fine during the whole affair and didn't even have trouble falling asleep. Either it was going to kill me or not, and if there was something I could do then I'd do whatever it takes, but I was not going to lose sleep over something that to me felt maybe like a 40 - 60% chance of it being cancer or nothing. A rational / stoic mindset about differentiation what you can and what you cannot control in your life and the knowledge to clearly separate those two helped me a lot with that I think.
To me it was not even remotely an option to tell her, I did what I think any good partner should have done in the situation I described above: Suck it up and don't let anything show. When I eventually told her afterwards she did get somewhat mad about it but conceded it was the right decision...
How could I even face myself in the mirror today if I had simply told her about it and she had failed her education as a result of it - especially after it turned out to be nothing (though even if it was cancer I think the same would apply)? I think I did precisely the right thing, what she would have wanted was irrelevant, the only person who really had "a choice" in this scenario was me.
Two counter-examples involving my SO in cases where we both chose option 1 and both felt it was the correct decision.
Event + option 1: I became aware I was pregnant with your child right before you left in order to visit your parents over the Christmas and New Year holidays. I kept it from you during all of your vacation because I knew it would screw up your whole stay with your parents and friends. I predicted you'd prefer to deal with it later and in person.
Event + option 1: I (not known to be paranoid about personal health) found a very suspicious lump in a very suspicious place in my body. I immediately went to get it checked, but since I predicted you'd be extremely worried about me I did not tell you about it until after my second check-up months later, so you would not have to worry about losing me to cancer like you recently did one of your parents.
We agree that in both cases these were good decisions, but those are rather extreme cases with a very high emotional cost to the other person compared to breaking a vase or something in the low range of suffering.
My suspicion: Preferring option 2 over option 1 across all applicable cases seems too generalized and wrong. I suspect there is a point of magnitude in emotional cost to another person, after which you might also feel that option 1 would be preferred by both parties - what do you think?
Another real-world-example I'm personally familiar with that feels very related to this one, but without the intention to ever let the emotionally impacted person actually know (i.e. direct lying) is this situation: Dear god-fearing bed-ridden grandma, your poor son died peacefully of a heart attack. (As opposed to slit his wrists in the bathroom while drunk).
Could very well be true. But it leaves open the curious question what on earth I would be looking for in the ex-eastern block ;)
Be honest, do you really actually fear cringing when you re-read your stuff months or years from now? Sounds to me like an invented reason to mask a much more plausible fear: Looking foolish in front of others by saying foolish things. Well in case you do make a fool of yourself you always have the option of admitting "back then I was foolish in saying that and I have changed my mind because of X". In this communuty being able to do that is usually accompanied with a slight status gain rather than severe status punishment and ridicule, so no need to worry about that.
Possible explanation: After a certain point of population growth the mice cannot keep track of all the individuals in their group (i.e. in the enclosure) and in nature this would usually result in a non-violent split of the population into two groups that go their own way. But with nowhere to go the mice created smaller subgroups that couldn't go anywhere yet still tried to maintain their own territory, mates etc. which led to conflict.
This would be analogous to humans having the mental capacity to keep up relations with something like 150 to 300 people. If primitive hunter gatherers grew beyond that limit it would result in the exodus of some part of that population into a new group that went elsewhere, probably mainly to retain group cohesion but in part also because the resources needed for survival at any one place were limited. The main reasons why we have not descended into intra-tribe violence once we started to live in permanent settlements and larger villages are probably social innovations as well as recognizing and sharing the benefits of larger scale village structures. Both these things seem to be beyond mouse brains.
Just brainstorming here.