Question

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was \bar {x} = 810 grams. This sample mean is an unbiased estimator of the mean weight \mu in the population of all ELBW babies. This means that

A. the average sample mean \bar {x}, over all possible samples, is equal to \mu.
B. the sample mean \bar {x} is always equal to \mu.
C. the sample mean \bar {x} will have a distribution that is close to Normal.
D. None of the above.

Answer 1

A. the average sample mean \bar {x}, over all possible samples, is equal to \mu.

Step-by-step explanation:

An unbiased estimator is a statistic that is expected to be close to the true value of the parameter being estimated. This means that, over many samples, the average of the sample means will be equal to the true population mean. In this case, the sample mean \bar{x} is an unbiased estimator of the population mean \mu for the weight of ELBW babies.