MS-DS Master of Data science MS-DS Master of Data science Statistical Inference Concepts Questions and Answers 3

Question 1

What is the interpretation of a p-value of 0.03 in a hypothesis test?

Accepted Answer

There is a 3% probability of observing data this extreme or more if the null hypothesis is true

Answer

There is a 3% chance the null hypothesis is true

Answer

The effect size is 3%

Answer

There is a 97% chance the alternative hypothesis is true

Question 2

Which estimator property ensures that the expected value of the estimator equals the true parameter?

Accepted Answer

Unbiasedness

Answer

Consistency

Answer

Efficiency

Answer

Sufficiency

Question 3

In Bayesian inference, what does the posterior distribution represent?

Accepted Answer

The updated belief about the parameter after observing data

Answer

The probability of the data given the parameter

Answer

The initial belief about the parameter before observing data

Answer

The marginal likelihood of the observed data

Question 4

What happens to the width of a confidence interval when the sample size is quadrupled?

Accepted Answer

It is reduced by half

Answer

It doubles

Answer

It remains the same

Answer

It is reduced by one quarter

Question 5

Which method provides the estimator with the lowest variance among all unbiased estimators?

Accepted Answer

Maximum likelihood estimation under regularity conditions

Answer

Method of moments

Answer

Ordinary least squares

Answer

Bayesian MAP estimation

Question 6

What does the Neyman-Pearson lemma establish about hypothesis testing?

Accepted Answer

The likelihood ratio test is the most powerful test for simple hypotheses at a given significance level

Answer

All hypothesis tests must use a significance level of 0.05

Answer

Bayesian tests are always superior to frequentist tests

Answer

Sample size does not affect the power of a test