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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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