Which of the following is a requirement for testing a claim about a population proportion?

• A. The data must be measured on an interval or ratio scale.
• B. The sample must be drawn from a normal distribution.
• C. The sample size must be large enough so that both $np$ and $n-np$ are at least 5.
• D. The population standard deviation must be known.

Answer: (C)

Verified step by step guidance

1. Understand that when testing a claim about a population proportion, the data are categorical (success/failure), so the measurement scale is not interval or ratio, but nominal.
2. Recognize that the sample does not need to be drawn from a normal distribution because the sampling distribution of the sample proportion can be approximated by a normal distribution under certain conditions.
3. Identify the key requirement: the sample size must be large enough so that both \(n p\) and \(n - n p\) are at least 5, where \(n\) is the sample size and \(p\) is the hypothesized population proportion.
4. This condition ensures that the sampling distribution of the sample proportion is approximately normal, which justifies using the normal approximation in hypothesis testing.
5. Note that knowing the population standard deviation is not required when testing a population proportion; this is a requirement for testing a population mean with a normal distribution.