Question

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Explanation:

Analyze the statement regarding sample size estimation

A sample size of 1,000 to 1,500 people is mathematically sufficient to estimate the opinions of a large national population (such as the United States) with a standard margin of error of approximately \(\pm 3\%\), provided the sample is randomly selected.

Evaluate the remaining statements

• "It is impossible to collect a random sample": Incorrect, as random digit dialing and probability-based sampling methods are standard scientific practices.
• "Public opinion surveys only tell you what the sample's opinions are, without providing any insight into the general population": Incorrect, because inferential statistics allows us to generalize sample findings to the broader population.
• "A sample refers to the group selected by a researcher to represent the most important characteristics of an entire population": Incorrect, as this describes purposive or quota sampling rather than the fundamental definition of a representative probability sample.

Answer:

• It is impossible to collect a random sample.
• It is possible to estimate the country's opinion based on a small sample of 1,000 to 1,500 people. (Correct answer)
• Public opinion surveys only tell you what the sample's opinions are, without providing any insight into the general population.
• A sample refers to the group selected by a researcher to represent the most important characteristics of an entire population.