Estimating Population Total with Square Root Transformation
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Questions and Answers

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?

  • 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?

  • 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?

    <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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