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 $x^{-}\overline{x}=810$grams. This sample mean is an unbiased estimator of the mean weight $\mu$ in the population of all ELBW babies, which means that

a. in all possible samples of size 219 from this population, the mean of the values of $x^{-}\overline{x}$will equal 810 .

b. in all possible samples of size 219 from this population, the mean of the values of ${\mathrm{x}}^{-\overline{x}}$will equal $\mu$

c. as we take larger and larger samples from this population, ${\mathrm{x}}^{-\overline{x}}$will get closer and closer to $\mu$.

d. in all possible samples of size 219 from this population, the values of $x^{-}\overline{x}$will have a distribution that is close to Normal.

e. the person measuring the children's weights does so without any error.

Short answer

(b). The mean of the values of in all feasible samples of size 219 from this population ${\mathrm{x}}^{-\overline{x}}$will equal $\mu$.

Step-by-step solution

Given Information

Given,

$$\begin{gathered} \overline{x}=810 \\ n=219 \end{gathered}$$

Explanation for correct option

For all conceivable samples of size n, this indicates that the population mean is equal to the average sample mean.

As a result, the most effective option is (b)

Explanation for incorrect option

a. in all possible samples of size 219 from this population, the mean of the values of ${\mathrm{x}}^{-\overline{x}}$will equal 810 is not the answer.

c. as we take larger and larger samples from this population, $\mathrm{x}-\overline{x}$will get closer and closer to $\mu$is not the answer.

d. in all possible samples of size 219 from this population, the values of ${\mathrm{x}}^{-}\overline{x}$will have a distribution that is close to Normal is not the answer.

e. the person measuring the children's weights does so without any error is not the answer.