The results of a poll show that between 43% and 55% of the population support an increase in sales tax to pay for a new sports stadium. a) What is the point estimate?

b) What is the margin of error?

Answers:

Explanation:

The point estimate is the midpoint of the two ends. We add up the endpoints and divide by 2 to get the midpoint. We have p = 0.43 and q = 0.55, so we get the midpoint (p+q)/2 = (0.43+0.55)/2 = 0.98/2 = 0.49, then this converts to 49%. Meaning 49% is exactly at the midway point of 43% and 55%

The margin of error is the distance from the midpoint to either endpoint. If we try to aim for 49%, but have some error, then we have an error of 55-49 = 6%, or we could say 49-43 = 6%; either way the margin of error is 6 percentage points.

The formula we can use is (q-p)/2 where p and q are the left and right endpoints of the interval. So in this case, we'd have,

(q-p)/2 = (0.55-0.43)/2 = 0.12/2 = 0.06 = 6% margin of error

Side note: We can think of it as if 49 is the center and 6 is the radius of the circle. We want to hit the center of the circle, but we have an error of 6 (meaning that's how far we could go in either direction).

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