To determine how many people will fall into a systematic sample if the general population consists of 500 people and we select every eighth person, we use the formula:

$\text{Sample size} = \frac{\text{Population size}}{\text{Interval size}}$

Here:

• Population size ($N$) = 500
• Interval size ($k$) = 8

$\text{Sample size} = \frac{500}{8} = 62.5$

Since the sample size must be a whole number, we typically round down (to ensure systematic intervals are maintained). Therefore, the sample size will be:

$62 \text{ people}$

This means the systematic sample will include 62 individuals from the population of 500.

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Related Questions:

1. What happens if the interval size is not an integer (e.g., selecting every 8.5th person)?
2. How do we ensure randomness in selecting the starting point for systematic sampling?
3. What are the advantages of systematic sampling compared to simple random sampling?
4. How do you adjust for systematic sampling if the population size isn’t perfectly divisible by the interval size?
5. Can systematic sampling introduce bias? If so, in what situations?

Tip: Systematic sampling works best when the population is evenly distributed; otherwise, it might introduce periodic bias.