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Why is it important to determine if the probability distribution of $\sqrt{Y_{\text{Tot}}}$ is unbiased?
Why is it important to determine if the probability distribution of $\sqrt{Y_{\text{Tot}}}$ is unbiased?
- To ensure that the estimator is consistent
- To check if the estimator provides unbiased estimates on average (correct)
- To guarantee that the estimator provides the best possible estimate
- To assess if the estimator tends to overestimate or underestimate
What is the focus of using the sample total based on Horvitz-Thompson estimator to estimate the square root of the population total?
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 mean of the population total
- Estimating the square root of the population total (correct)
- Estimating the median of the population total
- Estimating the range of the population total
What does it mean for an estimator to be unbiased in the context of this scenario?
What does it mean for an estimator to be unbiased in the context of this scenario?
- The estimator gives varying estimates of the population total
- The estimator provides on average correct estimates of the population total (correct)
- The estimator consistently overestimates the population total
- The estimator consistently underestimates the population total
How would a biased probability distribution of $\sqrt{Y_{\text{Tot}}}$ affect the estimation process?
How would a biased probability distribution of $\sqrt{Y_{\text{Tot}}}$ affect the estimation process?
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In the context of this scenario, what does calculating the variance of $\sqrt{Y_{\text{Tot}}}$ help in understanding?
In the context of this scenario, what does calculating the variance of $\sqrt{Y_{\text{Tot}}}$ help in understanding?
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