The estimator based on partial selection probabilities

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Reference no: EM131294581

Question 1:

Assume there are 25 school districts in the state of Colorado. Within each district, there are 16 high schools. Let the table of numbers below represent the average CSAP math score for 10th grades at each school. This table represents the entire population.

Consider a two-stage design with simple random sampling at each stage. At the first stage, select a SRS (wor) of S districts. From the ith selected district, select at SRS (wor) of 4 schools. Use a random number generator (or table) to make your selections. Explain in detail how you obtained this sample. Identify each selected school by circling its score in the table above. Estimate the average CASE math score pre school in the state of Colorado and the corresponding variance.

Question 2:

The region below is partitioned into 400 units and within each unit, the number of elk is known. This table represents the entire population.

Using a random number generator (or table), ake a SRS (wor) of 20 units from the population above. Explain in detail how you obtained this sample. Consider these 20 units as initial sample. Draw a dark box around these 20 initial units in the table above. If an initial unit contains at least one elk, use adaptive cluster sampling by sampling adjacent units (top, bottom, left, and right). Draw a dark circle around each of these additional units selected. Estimate the population total by using "draw-by¬draw intersections" (modified Hansen-Hurwitz estimator). Estimate the variance

Question 3:

The region below is partitioned into 400 units and within each unit, the number of elk is known. This table represents the entire population.

Using a random number generator (or table), take a SRS (wor) of 5 vertical strip plots from the population above. Explain in detail how you obtained this sample. Consider these 5 plots as initial sample. Draw a dark box around these 5 initial plots in the table above. If an initial plot contains a unit with at least one elk, use adaptive cluster sampling by sampling adjacent sampling (top, bottom, left, and right). Draw a dark circle around each of these additional units selected. Estimate the population total by using "the estimator based on partial selection probabilities" (modified Hansen-Hurwitz estimator). Estimate the variance

Question4: The region below is partitioned into 400 units and within each unit, the number of elk is known. Due to different types of terrain, this region has been partitioned nto two strata.

Using a random! umber generator (or tab e), take a SRS (wor) of 15 units from the stratum 1 (left) and a SRS (wor) of 10 units from stratum 2 (right). Explain in detail how you obtained this sample. Consider these units as initial sample. Draw a dark box around these initial units in the table above. If an initial unit contains at least one elk, use adaptive cluster sampling by sampling adjacent units (top, bottom, left, and right). You may crossover into the adjacent stratum. Draw a dark circle around each of these additional units selected. Estimate the population total by using "the estimator using expected numbers of initial intersections" (modified Hansen-Hurwitz estimator). Estimate the variance

Reference no: EM131294581

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