tutorial_9 - 2012/13Semester2 Tutorial9 ST3239 1(a...

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2012/13 Semester 2 Tutorial 9 ST3239 1. (a) Determine the variance of the two-stage estimator of population mean given in the PowerPoint slide in the event only one group with all its elements is selected, that is, in the event that m =1 and n i = N i . This is equivalent to cluster sampling with only one cluster is selected. (b) It is suggested that when each group is a “miniature” of the population with respect to a variable Y of interest, only one group with all its elements need to be selected since the sample average is the correct estimate of the population mean. This would appear to suggest that the variance in (a) ought to be zero. Is this impression justified? If not, how do you explain the apparent inconsistency? 2. In order to estimate the condition of highways under its jurisdiction and the cost of urgent repairs, the state Department of Transportation selected a number of “highway miles” in two stages. In the first stage, a number of highways were selected at random without replacement from the list of all highways maintained by the Department. In the
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