Sampling and Experiments · Challenge problem

A town has $900$ adults: $800$ have one phone line and $100$ have two. A pollster lists all $1000$ phone lines and calls lines chosen at random, so a person with two lines is twice as likely to be reached. Of the one-line adults $40\%$ support a proposal, and of the two-line adults $70\%$. By how many percentage points does the expected poll result exceed the true level of support in the town? Express your answer as a common fraction.