MS-DS Master of Data science Statistical and Probabilistic Analysis 5

Question 1

Which nonparametric test is the rank-based alternative to a paired t-test?

Accepted Answer

Wilcoxon signed-rank test

Answer

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:

Accepted Answer

X and Y are jointly normally distributed

Answer

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:

Accepted Answer

The credible interval directly states there is a 90% posterior probability the parameter lies in the interval

Answer

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:

Accepted Answer

The probability of obtaining a test statistic as extreme or more extreme than observed, assuming H₀ is true

Answer

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?

Accepted Answer

Exponential distribution

Answer

In a Poisson process, inter-arrival times are exponentially distributed with rate λ equal to the Poisson arrival rate.

MS-DS Master of Data science Practice Test