Statistical Inference Concepts Flashcards
7 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.
Read the first 7 Statistical Inference Concepts flashcards as text
A 95% confidence interval for the mean is [42, 58]. What is the correct interpretation?
Answer: If we repeated the sampling procedure many times, 95% of such intervals would contain the true mean
A confidence interval is a procedure: 95% of intervals constructed this way will capture the true parameter, not a probability statement about one specific interval.
Which of the following is a consequence of increasing the sample size in hypothesis testing while keeping α fixed?
Answer: Type II error rate decreases (power increases)
Larger samples reduce variance, making the test more sensitive and increasing statistical power (decreasing Type II error).
In a two-sided t-test with H₀: μ = 10 and a test statistic t = 2.1 (df=25), the p-value is approximately 0.046. At α = 0.05, what is the conclusion?
Answer: Reject H₀ because p < α
Since p ≈ 0.046 < 0.05 = α, we reject the null hypothesis at the 5% significance level.
The Neyman-Pearson lemma establishes that the likelihood ratio test is:
Answer: The most powerful test for a simple null versus a simple alternative
The Neyman-Pearson lemma proves that the likelihood ratio test is the most powerful test for comparing two simple (point) hypotheses.
A researcher uses bootstrapping to estimate the standard error of the median. What does this method fundamentally rely on?
Answer: Resampling with replacement from the observed data to approximate the sampling distribution
Bootstrapping treats the empirical distribution as a proxy for the population and resamples with replacement to build an approximate sampling distribution.
Which property ensures that a maximum likelihood estimator (MLE) achieves the Cramér-Rao lower bound asymptotically?
Answer: Asymptotic efficiency
MLEs are asymptotically efficient, meaning their variance achieves the Cramér-Rao lower bound in the limit of large samples.
In Bayesian inference, the posterior distribution is proportional to:
Answer: The likelihood times the prior
By Bayes' theorem, P(θ|data) ∝ P(data|θ) × P(θ), i.e., posterior ∝ likelihood × prior.