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I have problem understanding following example in parentheses. Maybe you can help me.

Ideally, researchers know the full extent of the population they want to study, and they can select a sample from this population at random. Statisticians can calculate the probability that such random samples represent the population; this is usually expressed in terms of sampling error (for example, there might be a 95 percent probability that the distribution of responses in a sample will be within 3 percent of the distribution in the population).

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The question in parentheses is incorrectly stated. It is not the distribution of response that can be said to be within x% of the population distribution with some probability, it is the estimate from the random sample that can be claimed to cover with an interval x% wide the true parameter value with a specified probability. The statement in bold in the parentheses is not understandable because it does not make sense as stated.

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  • $\begingroup$ Thanks michael. I have studied something about statistics at university, but i;m not a statistics professional. however, this phrase is stated in a book around social science $\endgroup$
    – Amir
    Aug 13, 2012 at 23:16
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    $\begingroup$ +1, throw away this book, it uses misleading language. Technically speaking, the design probabilities ARE the true probabilities, so one does not have to hide behind a shaky "repeated sampling" frequentist argument to justify the confidence intervals. $\endgroup$
    – StasK
    Aug 14, 2012 at 20:46

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