5.64. The 2006 publication Attitudes towards European Union Enlargement from Eurobarometer states, The readers are reminded that survey results arc estimations, the accuracy of which rests upon the sample size and upon the observed percentage. With samples of about 1,000 interviews, the real percentages vary within the following confidence limits:

Observed Limits 10% or 90%

20%, 80%

30%, 70%

40%, 60%

50%

±1.9

±2.5

±2.7

±3.0

±3.1

(a)

(b)

(c)

(d)

Explain how they got 3.0 points for 40%

or 60%.

Explain why the margin of error differs for different observed percentages.

Explain why the accuracy is the same for a particular percentage and for 100 minus that value (e.g., both 40% and 60%).

Explain why it is more difficult to estimate a population proportion when itis near 0.5 than when it is near 0 or 1.