Statistical Inference and Hypothesis Testing Flashcards

A permutation test determines the p-value by:

Answer: Repeatedly shuffling group labels and recomputing the test statistic to build a null distribution

Permutation tests approximate the null distribution empirically by randomly reassigning labels many times, making no distributional assumptions.

In the context of maximum likelihood estimation, the score function is:

Answer: The first derivative of the log-likelihood with respect to θ

The score function S(θ) = ∂ℓ/∂θ equals zero at the MLE and has expectation zero under the true parameter.

Which statement about bootstrap confidence intervals is TRUE?

Answer: They approximate the sampling distribution using resampling from observed data

Bootstrap intervals use repeated resampling with replacement to estimate the sampling distribution without relying on parametric assumptions.

A z-test for a proportion is valid when:

Answer: Both np and n(1−p) are at least 10, ensuring the normal approximation holds

The normal approximation to the binomial is reliable when np ≥ 10 and n(1−p) ≥ 10, ensuring enough expected successes and failures.

The Cramér-Rao lower bound gives the minimum variance achievable by:

Answer: Any unbiased estimator of a parameter

The CRLB states that Var(θ̂) ≥ 1/I(θ) for any unbiased estimator, where I(θ) is the Fisher information.

When conducting a one-way ANOVA F-test, rejecting H₀ tells you:

Answer: At least one group mean differs from the others

The ANOVA F-test only indicates that not all means are equal; post-hoc tests (e.g., Tukey HSD) are needed to identify which specific pairs differ.

In sequential hypothesis testing, the sequential probability ratio test (SPRT) allows:

Answer: Early stopping when accumulated evidence strongly favors H₀ or H₁

SPRT updates the likelihood ratio after each observation and stops sampling as soon as the ratio crosses predetermined boundaries for H₀ or H₁.