Final answer:
The p-chart is used in process sampling by attributes to monitor the proportion of defective items. It is applicable when the data recorded are categorical, allowing for a clear categorization of Success/Failure or Yes/No outcomes.
Step-by-step explanation:
The correct answer to the student's question is a) Process sampling by attributes. A p-chart is used in statistical quality control to monitor the proportion of defective items in a process. You know you are dealing with a proportion problem when the data are categorical, and consist of two categories such as Success/Failure or Yes/No. The p-chart assists in determining whether the proportion of defects is consistent with a stable process or if it has shifted in a way that requires attention.
The sample proportion (p') serves as the point estimate for the true population proportion, noted as p. When samples are taken from the production process, the number of defects (x) in each sample of size n is recorded, and the proportion of defects (p') is calculated by dividing x by n. According to the central limit theorem for proportions, as the sample size increases, the sampling distribution of the sample proportion will tend toward a normal distribution.