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

A p-value represents the probability of obtaining results as extreme as the observed data, assuming the null hypothesis is true.

Question 2

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

Accepted Answer

Unbiasedness

Answer

An unbiased estimator has an expected value exactly equal to the population parameter it estimates.

Question 3

In Bayesian inference, what does the posterior distribution represent?

Accepted Answer

The updated belief about the parameter after observing data

Answer

The posterior distribution combines prior beliefs with observed data through Bayes' theorem to give an updated probability distribution for the parameter.

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

The margin of error is proportional to 1 divided by the square root of n, so quadrupling n cuts the interval width in half.

Question 5

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

Accepted Answer

Maximum likelihood estimation under regularity conditions

Answer

Under regularity conditions, maximum likelihood estimators achieve the Cramér-Rao lower bound asymptotically, making them the most efficient unbiased estimators.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

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