MS-DS Master of Data science Statistical Inference Concepts Questions and Answers Flashcards
6 cards from real MS-DS Master of Data science practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
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What is the interpretation of a p-value of 0.03 in a hypothesis test?
Answer: There is a 3% probability of observing data this extreme or more if the null hypothesis is true
A p-value represents the probability of obtaining results as extreme as the observed data, assuming the null hypothesis is true.
Which estimator property ensures that the expected value of the estimator equals the true parameter?
Answer: Unbiasedness
An unbiased estimator has an expected value exactly equal to the population parameter it estimates.
In Bayesian inference, what does the posterior distribution represent?
Answer: The updated belief about the parameter after observing data
The posterior distribution combines prior beliefs with observed data through Bayes' theorem to give an updated probability distribution for the parameter.
What happens to the width of a confidence interval when the sample size is quadrupled?
Answer: It is reduced by half
The margin of error is proportional to 1 divided by the square root of n, so quadrupling n cuts the interval width in half.
Which method provides the estimator with the lowest variance among all unbiased estimators?
Answer: Maximum likelihood estimation under regularity conditions
Under regularity conditions, maximum likelihood estimators achieve the Cramér-Rao lower bound asymptotically, making them the most efficient unbiased estimators.
What does the Neyman-Pearson lemma establish about hypothesis testing?
Answer: The likelihood ratio test is the most powerful test for simple hypotheses at a given significance level
The Neyman-Pearson lemma proves that the likelihood ratio test maximizes power among all tests with the same significance level for testing simple hypotheses.