This set of 50 MCQs explores key concepts in hypothesis testing, including null and alternative hypotheses, p-values, test statistics, error types, and common tests like t-test, chi-square, and ANOVA. Designed for data analysts and statisticians to reinforce inferential statistics fundamentals.
1. The null hypothesis (H₀) is assumed:
✅ Correct Answer: a) True until evidence suggests otherwise
📝 Explanation:
Burden of proof lies on rejecting H₀.
2. A Type I error is:
✅ Correct Answer: a) Rejecting a true H₀
📝 Explanation:
False positive; probability = α (significance level).
3. The p-value represents:
✅ Correct Answer: b) Probability of data (or more extreme) given H₀
📝 Explanation:
Small p-value indicates evidence against H₀.
4. For a two-tailed test at α = 0.05, critical z-values are:
✅ Correct Answer: b) ±1.96
📝 Explanation:
2.5% in each tail of standard normal.
5. Power of a test is:
✅ Correct Answer: a) 1 – β (probability of rejecting false H₀)
📝 Explanation:
Higher power detects true effects.
6. Increasing sample size generally:
✅ Correct Answer: a) Increases power and narrows confidence intervals
📝 Explanation:
Standard error decreases as 1/√n.
7. A one-tailed test is appropriate when:
✅ Correct Answer: a) Direction of effect is specified in H₁
📝 Explanation:
All α in one tail; more powerful if direction correct.
8. The critical region is the set of test statistic values that lead to:
✅ Correct Answer: a) Rejection of H₀
📝 Explanation:
Defined by α and test type.
9. For unknown σ, mean test uses:
✅ Correct Answer: a) t-distribution
📝 Explanation:
df = n–1; approaches normal as n grows.
10. In A/B testing, H₀ typically states:
✅ Correct Answer: a) No difference in conversion rates (p_A = p_B)
📝 Explanation:
Rejection suggests statistically significant lift.
11. Effect size measures:
✅ Correct Answer: a) Magnitude of difference, independent of sample size
📝 Explanation:
E.g., Cohen’s d, odds ratio.
12. Practical significance differs from statistical significance because:
✅ Correct Answer: c) Both a and b
📝 Explanation:
Always report effect size with p-value.
13. The chi-square test for independence requires:
✅ Correct Answer: a) Expected frequencies ≥ 5 in most cells
📝 Explanation:
Ensures chi-square approximation validity.
14. Fisher’s exact test is preferred when:
✅ Correct Answer: a) Expected cell counts < 5
📝 Explanation:
Exact p-value for 2x2 tables.
15. ANOVA tests:
✅ Correct Answer: a) Equality of ≥3 population means
📝 Explanation:
F = MSB / MSW.
16. Post-hoc tests after ANOVA control:
✅ Correct Answer: a) Family-wise error rate (e.g., Tukey, Bonferroni)
📝 Explanation:
Identify which pairs differ.
17. Non-parametric alternative to one-sample t-test:
✅ Correct Answer: a) Wilcoxon signed-rank
📝 Explanation:
Tests if median differs from hypothesized value.
18. Mann-Whitney U tests:
✅ Correct Answer: a) Difference in distributions of two independent samples
📝 Explanation:
Non-parametric two-sample test.
19. The sign test uses:
✅ Correct Answer: d) Binomial distribution
📝 Explanation:
Simplest non-parametric paired test.
20. Equivalence testing aims to show:
✅ Correct Answer: a) Treatments are practically equivalent within margin
📝 Explanation:
TOST: two one-sided t-tests.
21. Superiority margin in clinical trials is denoted:
✅ Correct Answer: a) δ (non-inferiority if new ≥ old – δ)
📝 Explanation:
Pre-specified clinically meaningful difference.
22. Sequential testing (e.g., alpha spending) allows:
✅ Correct Answer: a) Early stopping for efficacy/futility
📝 Explanation:
Controls overall Type I error.
23. Multiple testing correction is needed when:
✅ Correct Answer: a) Performing many hypothesis tests simultaneously
📝 Explanation:
Inflates family-wise error rate.
24. Bonferroni correction adjusts α to:
✅ Correct Answer: a) α / m (m = number of tests)
📝 Explanation:
Conservative; controls FWER.
25. False Discovery Rate (FDR) controls:
✅ Correct Answer: a) Expected proportion of false positives among rejections
📝 Explanation:
Benjamini-Hochberg procedure.
26. In z-test for proportions, standard error is:
✅ Correct Answer: a) √[p₀(1–p₀)/n]
📝 Explanation:
Under H₀; p₀ is hypothesized proportion.
27. For small n and binary data, use:
✅ Correct Answer: a) Binomial test or Fisher’s exact
📝 Explanation:
Normal approximation unreliable.
28. The F-test compares:
✅ Correct Answer: a) Two population variances
📝 Explanation:
H₀: σ₁² = σ₂².
29. Levene’s test is robust to:
✅ Correct Answer: a) Non-normality when testing variance equality
📝 Explanation:
Uses absolute deviations from median.
30. Paired t-test assumes:
✅ Correct Answer: a) Differences are normally distributed
📝 Explanation:
df = n_pairs – 1.
31. Welch’s t-test adjusts for:
✅ Correct Answer: a) Unequal variances in two-sample means
📝 Explanation:
Uses Welch-Satterthwaite df.
32. McNemar’s test is for:
✅ Correct Answer: a) Paired binary data (before/after)
📝 Explanation:
Focuses on discordant pairs.
33. Cochran’s Q test extends McNemar to:
✅ Correct Answer: a) ≥3 related binary samples
📝 Explanation:
Non-parametric repeated measures.
34. The likelihood ratio test compares:
✅ Correct Answer: a) Fit of nested models
📝 Explanation:
–2(log L_reduced – log L_full) ~ χ².
35. Bayesian hypothesis testing uses:
✅ Correct Answer: a) Bayes factor (posterior odds / prior odds)
📝 Explanation:
BF > 10 strong evidence for H₁.
36. P-hacking refers to:
✅ Correct Answer: a) Manipulating analysis to obtain significant p-value
📝 Explanation:
Undermines scientific integrity.
37. Pre-registration combats p-hacking by:
✅ Correct Answer: a) Specifying analysis plan before seeing data
📝 Explanation:
Platforms: OSF, ClinicalTrials.gov.
38. Minimum detectable effect (MDE) is:
✅ Correct Answer: a) Smallest effect size with desired power
📝 Explanation:
Used in sample size calculation.
39. Sample size for mean test: n =
✅ Correct Answer: a) (z_{α/2} + z_β)² σ² / δ²
📝 Explanation:
δ = effect size; for two-sided.
40. For proportions, n ≈
✅ Correct Answer: c) Both depending on design
📝 Explanation:
Equal n per group uses pooled variance.
41. Peeking at data mid-trial inflates:
✅ Correct Answer: a) Type I error rate
📝 Explanation:
Requires alpha-spending functions.
42. O’Brien-Fleming boundary is:
✅ Correct Answer: a) Conservative early, liberal later in sequential trials
📝 Explanation:
Spends little alpha initially.
43. Cuped (Controlled-experiment Using Pre-experiment Data) reduces variance in A/B tests by:
✅ Correct Answer: a) Covariate adjustment with pre-period metric
📝 Explanation:
Y_adj = Y – θ (X_pre – μ_pre).
44. In multi-armed bandit, exploration-exploitation tradeoff is managed by:
✅ Correct Answer: a) Thompson sampling, epsilon-greedy
📝 Explanation:
Adaptive allocation to higher-performing arms.
45. Switchback tests are used in:
✅ Correct Answer: a) Time-based interference (e.g., network effects)
📝 Explanation:
Alternate treatment over time periods.
46. The z-test statistic for mean is:
✅ Correct Answer: a) (x̄ – μ₀) / (σ/√n)
📝 Explanation:
Known population σ.
47. Confidence interval and hypothesis test are related: if CI excludes μ₀, then:
✅ Correct Answer: a) Reject H₀: μ = μ₀ at corresponding α
📝 Explanation:
Duality: 95% CI ↔ two-tailed α=0.05 test.
48. A statistically significant result with p = 0.04 and tiny effect size may indicate:
✅ Correct Answer: a) Large sample detecting trivial difference
📝 Explanation:
Report confidence interval on effect.
49. Replication crisis highlights importance of:
✅ Correct Answer: a) Pre-registration, large n, effect sizes, open data
📝 Explanation:
Improves reproducibility and credibility.
50. The region of practical equivalence (ROPE) in Bayesian testing accepts H₀ if:
✅ Correct Answer: a) Posterior credible interval fully within ROPE
📝 Explanation:
Practical indifference zone around null.
