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