Chapter 7.3, Problem 67E

To determine

The correct answer from the options that 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 rake larger and larger samples from this population, the values of $\overline{x}$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.

Answer to Problem 67E

The correct answer is (b).

Explanation of Solution

Given information:

Mean weight, $\overline{x}=810$grams

Number of students in the random sample = 219

Here, the mean weight is $\overline{x}=810$and the sample size is $n=219$

It is known that the unbiased estimator of a mean weight is the sample mean which means, the population mean is equal to the average sample mean over all possible samples of size n.

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

Hence, the correct answer is (b).