Q.23 - The Practice of Statistics for AP

Question

If we take a simple random sample of size $n=500$ from a population of size $5,000,000$, the variability of our estimate will be

(a) much less than the variability for a sample of size $n=500$ from a population of size $50,000,000$. 

(b) slightly less than the variability for a sample of size $n=500$ from a population of size $50,000,000$.

(c) about the same as the variability for a sample of size $n=500$ from a population of size $50,000,000$.

(d) slightly greater than the variability for a sample of size $n=500$ from a population of size $50,000,000$.

(e) much greater than the variability for a sample of size $n=500$ from a population of size $50,000,000$. 

Step-by-Step Solution

Answer

A correct answer is an option (C) about the same as the variability for a sample of size $n=500$ from a population of size $50,000,000$.

Step 1: Given Information

A simple random sample of size $n=500$ from a population of size $5,000,000$, 

Step 2: Explanation

A simple random sample is expected to have roughly the same variability as its population and thus answer (c) is correct.