A confidence interval for a proportion based on a normal approximation is called?

A confidence interval for a proportion based on a normal approximation is called?

• A. Wald interval
• B. Wilson interval
• C. Agresti-Clemen interval
• D. Clopper-Pearson interval

Answer: (A)

The main idea is using a normal approximation to the binomial to form a confidence interval for a proportion. You take the sample proportion p-hat = X/n and use its approximate normal distribution with mean p and variance p(1−p)/n. Replacing p with p-hat gives the standard error sqrt(p-hat(1−p-hat)/n). With the normal quantile z for the desired confidence level, the interval is p-hat ± z * sqrt(p-hat(1−p-hat)/n). This is the Wald interval. It’s the classic method built directly from the normal approximation to the binomial. Keep in mind it can be less reliable for small n or when p is near 0 or 1, which is why other intervals (like Wilson or Agresti–Coull) are often preferred in practice. The Clopper–Pearson interval, by contrast, uses the exact binomial distribution rather than a normal approximation and tends to be more conservative.

The main idea is using a normal approximation to the binomial to form a confidence interval for a proportion. You take the sample proportion p-hat = X/n and use its approximate normal distribution with mean p and variance p(1−p)/n. Replacing p with p-hat gives the standard error sqrt(p-hat(1−p-hat)/n). With the normal quantile z for the desired confidence level, the interval is p-hat ± z * sqrt(p-hat(1−p-hat)/n). This is the Wald interval. It’s the classic method built directly from the normal approximation to the binomial.

Keep in mind it can be less reliable for small n or when p is near 0 or 1, which is why other intervals (like Wilson or Agresti–Coull) are often preferred in practice. The Clopper–Pearson interval, by contrast, uses the exact binomial distribution rather than a normal approximation and tends to be more conservative.