The thing about astronomy is that much of it is guesswork - albeit highly educated guesswork. This is because it is generally very difficult to do laboratory experiments on the scale required. And, with the exception of some particle physics and the odd space probe and lunar or Mars lander it is also difficult to 'go there and find out' or measure it.
Therefore most astronomy relies on observation and analysis of the various electromagnetic radiation waves and particles which are received at the Earth's surface, or satellites and high flying balloons and aircraft, as the case may be. Some of this can be extremely accurate, but much relies heavily on comparisons between similar data.
Hence when I studied astronomy (some 10-ish years ago) a general rule was that many astronomical measures and calculations were acceptable if they had an uncertainty of less than about a FACTOR of 10 (ten), i.e. if it was somewhere in the range of about a tenth to 10 times what it might be.
Distances and ages for stars and galaxies are particularly tricky to ascertain as they rely on comparisons between star brightness plus spectrum, and what is basically an empirically derived sequence of stellar evolution.
An example of this for distance is that the diameter of our own galaxy (Milky Way) is not exactly known, the best estimates I know of place it between 20 and 40 kpc in diameter. This is mainly due to line-of-sight issues, i.e. we can't really see through to the centre of the galaxy because of all the stuff (a highly technical term) in the way, together with dark matter issues.
So if you take a figure of 15,000,000,000 years old as meaning something in the region of, say, 10,000,000,000 to 30,000,000,000 years old, it sounds reasonably accurate.
Hope this is of some use. Cheers.