Add a test case for statistics logging.

I bumped into a crash (that has been fixed) in statistics logging. I figured a Python test case would be useful.

While I was there.. Waiting 5 seconds (i.e the smallest logging interval) for each different test isn't practical in the test suite. I dropped the minimum to 1 second. I figured if I wanted it to be 1 second for this case, other people probably will too.