Question

decide whether the statement below makes sense (or is clearly true) or does not make sense (or is clearly false). explain.
in my statistical study, i used a sample that was larger than the population

choose the correct answer below.

a. no, the statement does not make sense. the sample size should always equal the population size

b. yes, the statement makes sense. a sample can be as large as desired.

c. no, the statement does not make sense. a sample is a subset of the population and cannot be larger than the population

d. yes, the statement makes sense. a sample is always larger than the population

Explanation:

To determine if the statement makes sense, we recall the definitions: a population is the entire group being studied, and a sample is a subset of that population. By definition, a subset cannot be larger than the set it is a subset of. So a sample (subset of population) can't be larger than the population. Option A is wrong because sample size doesn't have to equal population size (we can have samples smaller than population). Option B is wrong as a sample's size is constrained by being a subset of the population. Option D is wrong as a sample is a subset, so it's smaller or equal (if sample is the whole population, but that's a census, not a typical sample). Option C correctly states the sample is a subset and can't be larger.

Answer:

C. No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population.