CQIA Statistical Methods 5 — Questions and Answers
Question 1: What is the primary purpose of a measurement system analysis (MSA) or gauge R&R study?
- To set process control limits
- To evaluate the accuracy and precision of a measurement system (Correct answer)
- To identify the root cause of defects
- To prioritize improvement opportunities
Correct answer: To evaluate the accuracy and precision of a measurement system
MSA/Gauge R&R quantifies how much of the observed variation comes from the measurement system itself versus the process.
Question 2: If a process has Cp = 1.5 and Cpk = 0.8, which conclusion is most accurate?
- The process spread is too wide for the spec
- The process is well-centered but has high variation
- The process is capable but not centered within specifications (Correct answer)
- Both Cp and Cpk indicate a capable process
Correct answer: The process is capable but not centered within specifications
Cp > 1 means the spread fits within specs, but Cpk < 1 means the process is shifted off-center toward a spec limit.
Question 3: Which of the following statements about the median is correct?
- It equals the mean in all distributions
- It is the most frequently occurring value
- It divides the dataset into two equal halves (Correct answer)
- It is always greater than the mode
Correct answer: It divides the dataset into two equal halves
The median is the middle value when data is sorted, dividing the distribution into two equal halves.
Question 4: In hypothesis testing, the p-value represents:
- The probability the null hypothesis is true
- The probability of observing the data if the null hypothesis were true (Correct answer)
- The significance level chosen by the analyst
- The effect size of the difference
Correct answer: The probability of observing the data if the null hypothesis were true
The p-value is the probability of getting results at least as extreme as observed, assuming the null hypothesis is true.
Question 5: Which of the following sampling methods ensures every possible sample of a given size has an equal chance of selection?
- Systematic sampling
- Stratified sampling
- Convenience sampling
- Simple random sampling (Correct answer)
Correct answer: Simple random sampling
Simple random sampling gives every possible combination of units an equal probability of being selected.
Question 6: On a control chart, which of the following indicates a process is out of statistical control?
- All points within control limits with no pattern
- A point beyond the upper control limit (Correct answer)
- Random scatter around the centerline
- Equal number of points above and below the mean
Correct answer: A point beyond the upper control limit
A point beyond a control limit is a signal of special cause variation, indicating the process is out of control.
Question 7: The mode of a dataset is best described as:
- The arithmetic average of all values
- The value that appears most frequently (Correct answer)
- The midpoint between the highest and lowest values
- The square root of the variance
Correct answer: The value that appears most frequently
The mode is the value (or values) that occur most often in a dataset, useful for categorical and discrete data.
CQIA Statistical Methods 5
What is the primary purpose of a measurement system analysis (MSA) or gauge R&R study?