There is an assumption that the sample group is random, normalised, or whatever the statistical term is.
Assuming that it is, then isn't it still the case that a sample size of 5000 will have a margin of error of around 1.5%, no matter what size the total population is?
Or is that formula wrong?
If the sample is small enough compared to the population (AM users), it doesn't matter how big the population is (the effect exists, it's just extremely small and lost in the error margins).
The error margin is 1.4% for 5000, 95% of the time. Which means 5% of the time, it will be off by more than 1.4%.
But, that's the easy part. Getting those 5000 to reflect AM users is the very very hard part.
If those 5000 for example are self-selected; right away it is a huge bias.
Most Apple Music users are probably casual, low involvement users, not the kind who would seek out a survey online (or even respond to an email about it).
Even if they had hit those 5000 correctly (random, unbiased), they'd still run into the second most common source of errors: really biased or leading questions or line of questioning. Tons of factors influence how we answer even the same questions (order is important).
That's why many polling from interested parties give then the answer they want to hear if they're at all involved in the wording of questions.
Most of those companies that get info online really have no clue how to build/conduct a proper survey that is actually reflective of reality. It's obvious the few time you actually see their methodology.