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Suppose a polling company carried a sample survey to examine the approval rate of a newly implemented public policy in a country. 1,600 citizens aged 18 and above were randomly selected in this survey. Among those, 640 approved the policy.

Choose one of the following options which is the most appropriate.

A. 40% of the citizens aged 18 and above in the country would approve the policy.

B. The estimation may be, on average, off by a margin of error of 2.4%.

C. One can say that the margin of error on the estimation is about 2.4% with a 95% confidence.

D. One may conclude that “there is a 95% chance that the policy approval rate in the population is between 37.6% ~ 42.4%.”

E. There is a no chance that majority (more than 50%) of the citizens aged 18 and above in the country would approve the policy as the result was obtained from a random sample which is representative of the population.

Ok so basically, I really have no idea how does a random polling affect anything. Can a random polling predict what will be actually happening on the ground?

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The problem is about margin of error –  The Chaz 2.0 Nov 15 '12 at 15:04
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(A) ignores sampling error. (B) and (D) are misinterpretations of margin of error--it's not an average (B), nor can we make probabilistic statements about the true proportion (if we're frequentists). (E) is false (it's very unlikely, but it is still possible that the true proportion is greater than 50%). The correct answer is (C).

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