BSE Engineering Statistics and Data-Driven Decision Making 2 — Questions and Answers
Question 1: A 95% confidence interval for the mean diameter of a part is (49.8 mm, 50.2 mm). Which interpretation is correct?
- 95% of all parts have diameters between 49.8 and 50.2 mm
- There is a 95% probability the true population mean is between 49.8 and 50.2 mm
- If the procedure were repeated many times, 95% of such intervals would contain the true mean (Correct answer)
- The sample mean will fall in this interval 95% of the time
Correct answer: If the procedure were repeated many times, 95% of such intervals would contain the true mean
A confidence interval is a procedure such that, in repeated sampling, 95% of constructed intervals will contain the true population mean.
Question 2: In statistical process control, a process is said to be 'in control' when:
- All output meets customer specifications
- Only common cause variation is present (Correct answer)
- Special cause variation is detected and removed
- Cp and Cpk are both greater than 2.0
Correct answer: Only common cause variation is present
A process is in statistical control when only common (random) cause variation is present, with no special (assignable) causes affecting the process.
Question 3: An engineer computes a p-value of 0.03 in a hypothesis test with a significance level of α = 0.05. The correct conclusion is:
- Fail to reject H₀ because 0.03 < 0.05
- Reject H₀ because 0.03 < 0.05 (Correct answer)
- Fail to reject H₀ because the difference is not practical
- Accept H₀ because the p-value is small
Correct answer: Reject H₀ because 0.03 < 0.05
When the p-value (0.03) is less than the significance level α (0.05), there is sufficient evidence to reject the null hypothesis.
Question 4: Which of the following is a nonparametric alternative to the one-sample t-test?
- F-test
- Chi-square goodness-of-fit test
- Wilcoxon signed-rank test (Correct answer)
- Two-proportion z-test
Correct answer: Wilcoxon signed-rank test
The Wilcoxon signed-rank test is the nonparametric equivalent of the one-sample t-test, used when normality cannot be assumed.
Question 5: Process capability index Cpk is different from Cp because Cpk:
- Uses the range instead of standard deviation
- Accounts for process centering relative to specification limits (Correct answer)
- Only applies to one-sided specifications
- Measures long-term capability rather than short-term
Correct answer: Accounts for process centering relative to specification limits
Cpk adjusts for how well-centered the process is between the specification limits, making it a more accurate measure when the process mean is not centered.
Question 6: In a multiple regression model, multicollinearity refers to:
- Non-linear relationships between predictor and response variables
- High correlation among independent predictor variables (Correct answer)
- Unequal variance of residuals across fitted values
- Autocorrelation in the residuals over time
Correct answer: High correlation among independent predictor variables
Multicollinearity occurs when two or more independent variables in a regression model are highly correlated, making it difficult to isolate their individual effects.
Question 7: Which data visualization technique is best suited for identifying the primary causes of a quality problem using the 80/20 rule?
- Scatter diagram
- Histogram
- Pareto chart (Correct answer)
- Control chart
Correct answer: Pareto chart
A Pareto chart ranks causes by frequency or impact, visually identifying the vital few causes (approximately 20%) that account for most (approximately 80%) of the problems.
BSE Engineering Statistics and Data-Driven Decision Making 2
A 95% confidence interval for the mean diameter of a part is (49.8 mm, 50.2 mm).
Which interpretation is correct?