Question

Is a sample of 500 volunteers a reliable measure for a population of 2,500?

Short answer

Yes, for a population of $2500$people, a sample size of$500$volunteers is a reliable metric.

Step-by-step solution

Introduction

When estimating unknown parameters, larger sample numbers often lead to greater precision. The rule of big numbers and the central limit theorem are two important principles of mathematical statistics that characterize this phenomena.

Explanation

A sample size of at least $10\%$of the population size is required.

Given a population of $2500$people, the $10\%$would be $250$.

As a result, a sample size of $250$is a good estimate of the population parameter. Any sample size more than $250$is also a good indicator.

For a population of $2500$, a sample size of $500$is a valid metric.