Estimating Population Total with Square Root Transformation
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Estimating Population Total with Square Root Transformation

This quiz covers the probability distribution of the sample total square root based on Horvitz-Thompson estimator, and determines if it is unbiased. It also involves calculating the variance of the square root of the population total.

Created by
@IlluminatingUtopia

Questions and Answers

Why is it important to determine if the probability distribution of $\sqrt{Y_{\text{Tot}}}$ is unbiased?

To check if the estimator provides unbiased estimates on average

What is the focus of using the sample total based on Horvitz-Thompson estimator to estimate the square root of the population total?

Estimating the square root of the population total

What does it mean for an estimator to be unbiased in the context of this scenario?

The estimator provides on average correct estimates of the population total

How would a biased probability distribution of $\sqrt{Y_{\text{Tot}}}$ affect the estimation process?

<p>It would introduce systematic errors in estimating the population total</p> Signup and view all the answers

In the context of this scenario, what does calculating the variance of $\sqrt{Y_{\text{Tot}}}$ help in understanding?

<p>The spread or variability of estimates around the true value</p> Signup and view all the answers

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