The question asks which of the given estimators is not unbiased for the corresponding population parameter. Here's the breakdown:

1. Sample Mean for Population Mean (a): The sample mean is an unbiased estimator of the population mean. It accurately reflects the population mean in expectation.

2. Sample Proportion for Population Proportion (b): The sample proportion is an unbiased estimator for the population proportion. It represents the true proportion in expectation.

3. Sample Variance for Population Variance (c): The sample variance is an unbiased estimator for the population variance because it is adjusted by dividing by $n-1$ (degrees of freedom) rather than $n$.

4. Sample Standard Deviation for Population Standard Deviation (d): This is not an unbiased estimator because the square root of an unbiased estimator (sample variance) does not guarantee unbiasedness. This introduces bias when estimating the population standard deviation.

Correct Answer: d. Sample Standard Deviation for Population Standard Deviation

Would you like further details or clarification?

Here are 5 related questions to expand your understanding:

1. What does it mean for an estimator to be unbiased?
2. Why is the adjustment by $n-1$ necessary for the sample variance to be unbiased?
3. How does bias affect the reliability of a statistical estimator?
4. Can you provide examples of biased estimators other than the standard deviation?
5. How do we compute the sample variance and its unbiased property?

Tip: Always check the mathematical definition of bias when working with estimators: an estimator is unbiased if its expected value equals the true parameter.