Bill W1AC wrote:

I think the only way to settle this question is to conduct a
well-designed survey with a ramdom sample of hams.

This one is tricky. With most surveys, there's no correlation between
the response rate and what you're trying to measure. If you're asking
for someone's opinion on an issue, you do a survey and get 10% response,
you can assume that the results are valid even though 90% of the people
who received the survey didn't bother to respond.

In a survey that asks licensed hams if they're active, if you get 10%
response, do you assume that the other 90% are inactive hams? No, you
can't do that. But you have to assume that an active ham is more likely
to respond to a survey about ham radio than an inactive one. Thus the
response is likely to be significantly skewed towards activity.

If there are any statisticians among the readers, please tell us how
many hams we'd have to sample to get a valid measurement.

For opinion surveys, the more you survey, the higher the accuracy. In
this case, I'm not sure that adding more people to the survey improves
the accuracy since active hams are more likely to respond. The key is
how to interpret the non-responders, something that seems unknowable.

I don't claim to be a statistician, so I would appreciate comments from
someone who is.

73, Steve KB9X