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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 $\stackrel{¯}{x}=810$ grams. This sample mean is an unbiased estimator of the mean weight$\mathrm{μ}$ 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 $\stackrel{¯}{x}$ will equal $810$ .

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

(c) as we take larger and larger samples from this population, $\stackrel{¯}{x}$ will get closer and closer to $\mathrm{μ}$.

(d) in all possible samples of size $219$ from this population, the values of $\stackrel{¯}{x}$ 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

01

Given Information

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

The sample size is $n=219$.

02

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 $\mathrm{μ}$ in all feasible size $219$ samples from this population.

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