In the context of a $p$ chart, which of the following best describes the assumption about the sample size for each subgroup?

• A. The sample size for each subgroup is constant.
• B. The sample size for each subgroup can vary widely without affecting the chart.
• C. The sample size must always be less than $10$.
• D. The sample size is assumed to be unknown.

Answer: (A)

Verified step by step guidance

1. Understand that a p chart (proportion chart) is used to monitor the proportion of defective items in a process over time, where data is collected in subgroups or samples.
2. Recognize that the calculation of control limits in a p chart depends on the sample size of each subgroup because the variability of the proportion is influenced by the number of observations.
3. Recall the formula for the standard error of the proportion in a p chart: \(\sqrt{\frac{p(1-p)}{n}}\), where \(p\) is the average proportion defective and \(n\) is the sample size of the subgroup.
4. Note that if the sample size varies widely between subgroups, the control limits would also vary, making the chart harder to interpret and less reliable.
5. Therefore, the standard assumption for a p chart is that the sample size for each subgroup is constant, ensuring consistent control limits and meaningful comparison across subgroups.