a) Why is an unbiased statistic generally preferred over a biased statistic for estimating a population characteristic? An unbiased statistic is generally preferred over a biased one because the...

a) Why is an unbiased statistic generally preferred over a biased statistic for estimating a population characteristic?

An unbiased statistic is generally preferred over a biased one because the unbiased statistic , on average, give the correct value for the population characteristic being estimated, while the biased one .

(b) Does unbiasedness alone guarantee that the estimate will be close to the true value? Explain.

Unbiasedness alone guarantee that the value of the statistic will be close to the true value of the population characteristic, since, if the statistic has a large standard deviation, values of the statistic will tend to be the population characteristic.

(c) Under what circumstances might you choose a biased statistic over an unbiased statistic if two statistics are available for estimating a population characteristic?

A biased statistic might be chosen in preference to an unbiased one if the biased statistic has a standard deviation than that of the unbiased statistic, and as a result values of the biased statistic are more likely to be the population characteristic than values of the unbiased statistic.