MS-DS Master of Data science Statistical and Probabilistic Analysis 5 — Questions and Answers
Question 1: Which nonparametric test is the rank-based alternative to a paired t-test?
- Wilcoxon signed-rank test (Correct answer)
- Mann-Whitney U test
- Kruskal-Wallis test
- Friedman test
Correct answer: Wilcoxon signed-rank test
The Wilcoxon signed-rank test analyzes paired differences using ranks, making it the nonparametric equivalent of the paired t-test.
Question 2: If X and Y are jointly distributed random variables, Cov(X, Y) = 0 implies independence only when:
- X and Y are jointly normally distributed (Correct answer)
- X and Y have the same marginal distribution
- X and Y are both discrete
- X and Y share a common support
Correct answer: X and Y are jointly normally distributed
Zero covariance implies independence only for jointly normal distributions; in general, uncorrelated does not mean independent.
Question 3: A 90% credible interval in Bayesian statistics differs from a 90% confidence interval in that:
- The credible interval directly states there is a 90% posterior probability the parameter lies in the interval (Correct answer)
- The credible interval is always wider than the confidence interval
- The credible interval requires normality of the data
- The credible interval is based on resampling the data
Correct answer: The credible interval directly states there is a 90% posterior probability the parameter lies in the interval
A Bayesian credible interval has a direct probability interpretation: given the prior and data, P(θ ∈ interval) = 90%.
Question 4: In hypothesis testing, the p-value is defined as:
- The probability of obtaining a test statistic as extreme or more extreme than observed, assuming H₀ is true (Correct answer)
- The probability that the null hypothesis is true
- The probability the alternative hypothesis is true
- One minus the confidence level
Correct answer: The probability of obtaining a test statistic as extreme or more extreme than observed, assuming H₀ is true
The p-value is a conditional probability computed under H₀; small p-values suggest the observed data are unlikely under the null.
Question 5: Which distribution is appropriate for modeling the time between events in a Poisson process?
- Exponential distribution (Correct answer)
- Binomial distribution
- Normal distribution
- Geometric distribution
Correct answer: Exponential distribution
In a Poisson process, inter-arrival times are exponentially distributed with rate λ equal to the Poisson arrival rate.
Question 6: A confusion matrix shows: TP=80, FP=20, FN=10, TN=90. What is the precision of the classifier?
- 0.80 (Correct answer)
- 0.89
- 0.88
- 0.73
Correct answer: 0.80
Precision = TP / (TP + FP) = 80 / (80 + 20) = 80/100 = 0.80.
Question 7: The F-statistic in ANOVA is the ratio of:
- Between-group variance to within-group variance (Correct answer)
- Sample variance to population variance
- Explained variance to total variance
- Between-group mean to within-group mean
Correct answer: Between-group variance to within-group variance
F = Mean Square Between / Mean Square Within; a large F suggests group means differ more than expected by chance.
MS-DS Master of Data science Statistical and Probabilistic Analysis 5
Which nonparametric test is the rank-based alternative to a paired t-test?