Question

Which of the following statements best distinguishes between unbiased and biased estimators in statistics?

a. Unbiased estimators tend to consistently overestimate the parameter of interest, while biased estimators tend to underestimate.
b. Unbiased estimators, on average, tend to be closer to the true population parameter, whereas biased estimators systematically deviate from it.
c. Unbiased estimators always have a smaller variance compared to biased estimators.
d. Biased estimators provide a more accurate estimation in small sample sizes compared to unbiased estimators.

Answer 1

The best distinction between unbiased and biased estimators is that unbiased estimators are generally consistent with the true population parameter, while biased estimators have systematic deviations.

Step-by-step explanation:

The statement that best distinguishes between unbiased and biased estimators in statistics is: 'Unbiased estimators, on average, tend to be closer to the true population parameter, whereas biased estimators systematically deviate from it.'

An unbiased estimator is a statistic that will, on average, hit the target population parameter if we could take an infinite number of samples and calculate the estimator for each one. It doesn't systematically overestimate or underestimate the parameter. By contrast, a biased estimator has a systematic error, consistently either overestimating or underestimating the population parameter.

Using a biased estimator can lead to incorrect conclusions about the population. This is why sampling must be done carefully to ensure a representative and unbiased sample. Larger samples can reduce chance error but cannot overcome bias if the sampling method itself is flawed. Hence, the importance of random selection and absence of bias in sampling cannot be overstressed.

Confidence intervals and hypothesis testing are two principal methods used in inferential statistics to estimate and make inferences about population parameters based on sample data.