Q.67 - The Practice of Statistics for AP

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 $\overline{x}=810$ 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 $\overline{x}$ will equal $810$ .

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

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

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

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

Step-by-Step Solution

Answer

The correct answer is (b).

Step 1: Given Information

The mean weight is $\overline{x}=810$ ,

The sample size is $n=219$.

Step 2: Explanation

The population means is equal to the average sample mean overall feasible samples of size $n$, which is known as the unbiased estimator of a mean weight.

The mean values of $\overline{x}$ will equal $\mu$ in all feasible size $219$ samples from this population.