sampling distributions for proportions

The conditions are not met, because n(1 - p) = 42.5, so a t-distribution should be used instead.

The conditions are met, because np = 7.5 is close enough to 10 for a normal model to work.

The conditions are met, because n = 50 is greater than 30, so the normal model applies.

The conditions are not met, because np = 7.5 is less than 10, so the normal model is unreliable.

The conditions are met, because n(1 - p) = 42.5 is at least 10, and one count is enough.

It is not wrong, because a result of 0.53 or more occurs about 10% of the time when p = 0.51.

The poll was wrong, because any sample proportion that differs from p shows an error in the poll.

The poll was wrong, because a sample proportion that overstates support shows the poll was biased.

The poll was wrong, because z is about 1.27, which is greater than 1 and so shows a real difference.

The poll was right, because the election count should have matched 53 percent.