MS-DS Master of Data science Statistical Inference Concepts 5

Question 1

The Kolmogorov-Smirnov test is used to:

Accepted Answer

Test whether a sample comes from a specified distribution or compare two samples

Answer

The KS test compares the empirical CDF against a theoretical CDF (one-sample) or between two empirical CDFs (two-sample) to detect distributional differences.

Question 2

In maximum likelihood estimation, the score function is defined as:

Accepted Answer

The gradient of the log-likelihood with respect to the parameter

Answer

The score is ∂ℓ(θ)/∂θ, the first derivative of the log-likelihood; at the MLE it equals zero.

Question 3

When using the Wilcoxon signed-rank test instead of a paired t-test, the primary reason is:

Accepted Answer

The Wilcoxon test does not assume normality and is more robust to outliers

Answer

The Wilcoxon signed-rank test is a non-parametric alternative that only assumes symmetry of differences, making it robust when normality is violated.

Question 4

In the context of regression, what does the term 'heteroscedasticity' refer to?

Accepted Answer

Error variance that changes across levels of the predictors

Answer

Heteroscedasticity means the variance of the regression errors is not constant (σᵢ² varies with X), violating the homoscedasticity assumption of OLS.

Question 5

Which of the following is the correct formula for the standard error of a proportion p̂ estimated from n observations?

Accepted Answer

√(p̂(1−p̂)/n)

Answer

For a binomial proportion, SE(p̂) = √[p̂(1−p̂)/n], derived from the variance of the Bernoulli distribution divided by n.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Statistical Inference Concepts 5