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. yes, the statement makes sense. a sample can be as large as desired.
b. yes, the statement makes sense. a sample is always larger than the population.
c. no, the statement does not make sense. a sample is a subset of the population and cannot be larger than the population.
d. no, the statement does not make sense. the sample size should always equal the population size.

Explanation:

Define population and sample

$$ \text{Population} = \text{The entire group of individuals or instances under study.} $$

$$ \text{Sample} = \text{A subset of the population selected for analysis.} $$

Determine the relationship between sizes

$$ \text{Sample} \subseteq \text{Population} \implies \text{Size of Sample} \le \text{Size of Population} $$

Evaluate the given statement

$$ \text{Statement: "I used a sample that was larger than the population."} \implies \text{False (Does not make sense)} $$

Answer:

• A. Yes, the statement makes sense. A sample can be as large as desired.
• B. Yes, the statement makes sense. A sample is always larger than the population.
• C. No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population. (Correct answer)
• D. No, the statement does not make sense. The sample size should always equal the population size.