Question

Under which condition is the sample mean, , a point estimate of the population proportion?

Answer 1

answer choices (please post these next time)

A.
The sample size, n, is small enough.
B.
The sample represents a proportion of the population.
C.
The sample proportion is unbiased.
D.
The sample proportion is never a point estimate of the population proportion.

Answer 2

the point of taking a sample, and measuring statistics on that sample, is to make some conclusion about the whole population. in order for these conclusions to be valid, the sample needs to be representative of the population.

going through the choices

A: incorrect. a small but un-representative sample would not lead to a valid conclusion about the whole population.

B: by definition all samples represent a proportion of the population. this is not enough to make the sample mean a good point estimate. incorrect.

D: this is also incorrect. as we stated, a sample mean *can* be a point estimate if the sample is representative of the population.

therefore, the only correct response is C. in order for a sample to be representaive of the population, it has to be selected randomly (a.k.a in an unbiased manner).