Which of the following are assumptions required for conducting a significance test for a population proportion?

• A. The population standard deviation is known.
• B. The data must be normally distributed regardless of sample size.
• C. The sample size must always be less than $30$.
• D. The sample is randomly selected from the population.

Answer: (D)

Verified step by step guidance

1. Understand that when conducting a significance test for a population proportion, certain assumptions must be met to ensure the validity of the test results.
2. Recognize that the population standard deviation being known is an assumption related to tests about population means, not proportions, so it is not required here.
3. Know that the data for a population proportion test do not need to be normally distributed; instead, the sampling distribution of the sample proportion should be approximately normal, which is generally ensured by a sufficiently large sample size.
4. Recall that the sample size does not have to be less than 30; in fact, for proportion tests, a larger sample size is often necessary to satisfy the normal approximation conditions (usually both \( np \) and \( n(1-p) \) are at least 10).
5. Identify that the key assumption is that the sample is randomly selected from the population, which ensures that the sample is representative and that the inference is valid.