Question

Define the difference estimator for the population mean. Show that it is an unbiased estimator and its variance is given by equationwhere symbols have their usual meanings. 

29 Apr 2025
Answer :
Word Count : 280
The difference estimator for the population mean is used when there is an auxiliary variable $X$ correlated with the study variable $Y$. Let the population consist of $N$ units, and a sample of size $n$ is drawn. Denote the population means as $\bar{Y}$ and $\bar{X}$, and the sample means as $\bar{y}$ and $\bar{x}$. The difference estimator _________ _____ ____ _____ _______ _________ _________ __________ _________ _______ _____ _______.
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