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.

Step by step solution

01

Given Information

Given,

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

02

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)

03

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.

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