Question

A newborn baby has extremely low birth weight 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 810 grams. This sample mean is an unbiased estimator of the mean weight m in the population of extremely low birth weight babies. This means that:
a. when the sample is a simple random sample from the population, the mean of the sampling distribution of the sample mean is the same as the population mean.
b. as we take larger and larger samples from this population the sample mean, x-bar, will get closer and closer to the population mean.
c. in many samples from this population, the many values of x-bar will have a distribution that is close to Noral.
d. in many births from this population the many values of x-bar will be equal to m.

Answer 1

Answer:

Option b is right

Step-by-step explanation:

Given that a newborn baby has extremely low birth weight 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 810 grams.

When this  sample mean is an unbiased estimator of the mean weight m in the population of extremely low birth weight babies, this implies that

$E(\bar x) = \mu$

i.e. averages of all sample means will equal to population mean.

Hence correct option would be

b. as we take larger and larger samples from this population the sample mean, x-bar, will get closer and closer to the population mean.