# Applied Survey Methods: A Statistical Perspective (Wiley by Jelke Bethlehem

By Jelke Bethlehem

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Extra info for Applied Survey Methods: A Statistical Perspective (Wiley Series in Survey Methodology)

Example text

Reprinted by permission of Imre Kortbeek. 4 A 20-sided dice. be selected from a population of size 750. In this case, a coin and a dice cannot be used. What can be used is a 20-sided dice; see Fig. 4. Such a dice contains the numbers from 1 to 20. If 10 is subtracted from the outcomes of 10 and higher, and 10 is interpreted as 0, then the dice contains twice the numbers from 0 to 9. Three throws of such a dice produce a three-digit number in the range from 0 to 999. If the outcome 0 and all outcomes over 750 are ignored, a sequence number of an element is obtained.

Suppose a population consists of four elements: U ¼ {1, 2, 3, 4}. 7 A roulette: a sample with replacement. Reprinted by permission of Imre Kortbeek. There are some situations in practice where sampling with replacement is preferred. This is the case for samples selected with unequal probabilities. 3. A sample with replacement can also be represented by a sequence of indicators a ¼ (a1, a2, . , aN). But now every indicator ak can assume the values 0, 1, 2, . , n. A roulette wheel is a good example of sampling with replacement.

Either a more reliable conclusion can be drawn about a less precise estimate, or a less reliable conclusion is drawn about a more precise estimate. The confidence interval can only be computed if the value S(t) of the standard error is known. This is generally not the case, because it requires knowledge of all possible values of the estimator. The distribution of the estimator can only be computed if all values of Y in the population are known. If all these values were known, there was no need to carry out the survey.