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

• A. The test statistic for a proportion is calculated using the sample mean and sample standard deviation.
• B. The sampling distribution of the sample proportion can be approximated by a normal distribution if both $n\times p$ and $n\times (1-p)$ are at least 5.
• C. The null hypothesis is typically stated as $p=p_0$, where $p_0$ is the claimed population proportion.
• D. A significance level $\alpha$ is chosen before collecting data to determine the rejection region.

Answer: (A)

Verified step by step guidance

1. Understand that when testing a claim about a population proportion, the test statistic is based on the sample proportion \( \hat{p} \), not the sample mean or sample standard deviation.
2. Recall that the test statistic for a population proportion is calculated using the formula: \[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \] where \( \hat{p} \) is the sample proportion, \( p_0 \) is the hypothesized population proportion, and \( n \) is the sample size.
3. Recognize the conditions for approximating the sampling distribution of \( \hat{p} \) by a normal distribution: both \( n \times p_0 \) and \( n \times (1 - p_0) \) must be at least 5 to ensure the normal approximation is valid.
4. Note that the null hypothesis in proportion testing is typically stated as \( H_0: p = p_0 \), where \( p_0 \) is the claimed population proportion.
5. Remember that the significance level \( \alpha \) is chosen before collecting data to define the rejection region, which helps decide whether to reject the null hypothesis based on the test statistic.