Which of the following is not true when testing a claim about a population proportion?

• A. The normal approximation can be used only if both $np$ and $n-np$ are at least 5.
• B. The null hypothesis always states that the population proportion is less than a specific value.
• C. The sample should be randomly selected from the population.
• D. The test statistic is calculated using the hypothesized population proportion.

Answer: (B)

Verified step by step guidance

1. Understand the context: When testing a claim about a population proportion, certain conditions and definitions must be met to ensure the validity of the test.
2. Recall the condition for using the normal approximation in proportion tests: Both \(n \hat{p}\) and \(n - n \hat{p}\) (where \(n\) is the sample size and \(\hat{p}\) is the hypothesized population proportion) should be at least 5 to justify the approximation to the normal distribution.
3. Remember the role of the null hypothesis (\(H_0\)): It typically states that the population proportion is equal to a specific value, not less than or greater than. Inequalities are usually part of the alternative hypothesis (\(H_a\)).
4. Confirm that the sample should be randomly selected to ensure that the results are representative and the inference is valid.
5. Note that the test statistic for a proportion test is calculated using the hypothesized population proportion from the null hypothesis, not the sample proportion.