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In an aerial survey of four plots selected by SRS, the numbers of ducks detected were 44, 44, 4, and 16. Careful examinations of photoimagery

In an aerial survey of four plots selected by SRS, the numbers of ducks detected were 44, 44, 4, and 16. Careful examinations of photoimagery of the first and third of these plots (selected as a simple random subsample) revealed that the actual presence of 56 and 6 ducks respectively. The study area consists 10 plots.
a)Estimate the total number of ducks in the study area by using a ratio estimator. Estimate the variance of the estimator.
b)Suppose the photo analysis doubles the cost of observing a plot. Estimate the optimal subsampling fraction.
5. (Adapted from Exercise 14.1 of Thompson (1992) ) In an aerial survey of four plots selected by SRS, the numbers of ducks detected were 44, 44, 4, and 16. Careful examinations of photoimagery of the first and third of these plots (selected as a simple random subsample) revealed that the actual presence of 56 and 6 ducks respectively. The study area consists 10 plots. (a) Estimate the total number of ducks in the study area by using a ratio estimator. Estimate the variance of the estimator.(b) Suppose the photo analysis doubles the cost of observing a plot. Es- timate the optimal subsampling fraction

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