CQIA Statistical Methods 3 — Questions and Answers
Question 1: What is the purpose of stratification in data analysis?
- To calculate the average of a dataset
- To separate data into subgroups to identify patterns (Correct answer)
- To create control limits for a process
- To rank defects by frequency
Correct answer: To separate data into subgroups to identify patterns
Stratification divides data into meaningful subgroups (by shift, machine, operator) to reveal hidden patterns.
Question 2: An X-bar chart is used to monitor which characteristic of a process?
- Process variation within subgroups
- The average (mean) of subgroup measurements (Correct answer)
- The proportion of defective items
- The count of defects per unit
Correct answer: The average (mean) of subgroup measurements
An X-bar chart tracks the subgroup average over time to detect shifts in process centering.
Question 3: Which statistical tool displays the frequency distribution of continuous data?
- Pareto chart
- Scatter diagram
- Histogram (Correct answer)
- Control chart
Correct answer: Histogram
A histogram displays how continuous data is distributed across intervals (bins), showing shape and spread.
Question 4: The interquartile range (IQR) is calculated as:
- Maximum minus minimum
- Third quartile minus first quartile (Correct answer)
- Mean minus median
- Standard deviation times two
Correct answer: Third quartile minus first quartile
IQR = Q3 − Q1, representing the spread of the middle 50% of data and is resistant to outliers.
Question 5: A c-chart is most appropriate when:
- Subgroup sizes vary
- Tracking proportion defective
- Counting defects per unit with constant sample size (Correct answer)
- Measuring continuous data
Correct answer: Counting defects per unit with constant sample size
The c-chart monitors the count of defects per unit when the opportunity for defects is constant.
Question 6: Process capability index Cpk differs from Cp because Cpk:
- Only considers process spread
- Accounts for both spread and process centering (Correct answer)
- Uses customer specifications only
- Is calculated from control chart limits
Correct answer: Accounts for both spread and process centering
Cpk accounts for how centered the process is relative to specification limits, while Cp only considers spread.
Question 7: Which of the following best describes a Type II error in hypothesis testing?
- Rejecting a true null hypothesis
- Failing to reject a false null hypothesis (Correct answer)
- Setting alpha too high
- Using the wrong test statistic
Correct answer: Failing to reject a false null hypothesis
A Type II error (beta error) occurs when you fail to detect a real effect — accepting a false null hypothesis.
CQIA Statistical Methods 3
What is the purpose of stratification in data analysis?