roughly 50% likely to be true or false

I feel like you'd need to specify for what kind of person these statements shall appear about 50% likely. That can be very different across different knowledge backgrounds. I, as a European, have no idea whether or not Iowa and Ohio are neighboring states.

That said, I think geographical questions might do well because such statements should be easy to generate and find evidence for/against.

Examples:

• The Great Slave Lake is the 11th largest lake in the world
• Algeria is the 12th largest country in the world
• Israel is bigger than New Jersey
• Germany is smaller than Montana
• Sulawesi is one of the ten largest islands in the world

(some of these are false, some are true).

To create these statements, one could look up wikipedia lists, e.g.List of islands by area, List of countries by area, List of rivers by length and so on.

Writing a script that extracts statements from this type of data should be feasible, and one could write it such that for each true statement extracted, a wrong statement is created as well.

I find it very hard to judge these questions, however given a world map (without borders) this changes. Also, you could tell me how many people live in the countries/states mentioned, how large one of this countries is in absolute numbers or what the greatest depth of the Great Slave Lake and fifteen other lakes in the world is.

Once these statements are available, they could not only be used for calibration training, but also for exercises about seeking the truth in groups.