The kanji say it all. Half-faith, half doubt. This yo-ji is attached to です、or で and though it starts with faith, it seems to just boil down to a matter of doubt. .
1. Unsure of what to believe.
2. Half-convinced; half-doubtful
3. To be skeptical.
Most of the online examples I've found are situations that we would translate simply as 'doubt' or 'skepticism:'
I don't know if I can do it, but I'm gonna try.
to be in disbelief regarding so and so's age.
When you first get diagnosed by a doctor, take it with a grain of salt because... it's better to critically evaluate things... *
Learning this one makes me wish I had a transcript of some of the lessons we heard at the zazen retreat in Oita, because I'm sure that the Reverend Paul must have used it when he said the Japanese version of this: "You'll know that you'll be able to learn from a Buddhist teacher if you can do two things: Accept and believe everything he says as absolutely true without exception and also, immediately reject everything he says as bullshit, without exception." Sounds like a super literal version of 半信半疑 to me.
Your reason for being late makes me incredulous. Were you really attacked by a freaky demon crab?
(If so you should attack his weak point for massive damage.)
*(Okay... just a quick and WAY overdue note about my translations: They can probably be translated better. I tend to try and capture the sentiment instead of what is literally being said. I don't know if that makes me a good translator or a bad one, but I'm sure that if you were to RE-cast my translated English into Japanese, they wouldn't come out the same. A more literal translation of that doctor statement would be "When you first get diagnosed by a doctor, be half convinced and half doubtful, because it's better to have a skeptical feeling, I think.")