Confidence intervals for population proportions are used when the data satisfies all the requirements for the binomial distribution. Specifically, the sample data must meet these conditions:

1. The sample must be random.
2. The sample size must be large enough such that both $np \geq 5$ and $n(1-p) \geq 5$, where $n$ is the sample size and $p$ is the sample proportion.
3. The population size must be at least 10 times larger than the sample size.

When these conditions are satisfied, the sample proportion can be approximated by a normal distribution due to the Central Limit Theorem. This allows us to use the normal distribution to construct confidence intervals for the population proportion.

Would you like further details on how the confidence interval for a population proportion is calculated?

Here are five related questions:

1. How do you calculate a confidence interval for a population proportion?
2. What is the formula for the standard error in a population proportion confidence interval?
3. What does it mean if a confidence interval includes 0 or 1 in a population proportion context?
4. How does increasing the sample size affect the confidence interval for a population proportion?
5. What is the z-value in a confidence interval for proportions, and how is it determined?

Tip: The larger your sample size, the narrower your confidence interval will be, leading to a more precise estimate of the population proportion.