Hypothesis Testing MCQs 2026

The null hypothesis H0 typically represents

1. A a statement of no effect, no difference, or a specified parameter value ✓
2. B the research claim always ✓
3. C the alternative only ✓
4. D the p-value ✓

The alternative hypothesis Ha may be

1. A one-sided or two-sided depending on the research question ✓
2. B always two-sided only ✓
3. C always μ = 0 ✓
4. D always the confidence interval ✓

Type I error is

1. A failing to reject a false H0 ✓
2. B rejecting H0 when H0 is true ✓
3. C accepting Ha when Ha is false only ✓
4. D computing a CI ✓

Type II error is

1. A rejecting true H0 ✓
2. B setting confidence level ✓
3. C choosing sample size only ✓
4. D failing to reject H0 when H0 is false ✓

The significance level α is

1. A the probability of Type II error ✓
2. B the maximum acceptable probability of Type I error ✓
3. C the p-value always ✓
4. D the power of the test ✓

The p-value is

1. A the probability, assuming H0 is true, of obtaining a test statistic at least as extreme as observed ✓
2. B the probability H0 is true ✓
3. C the same as α always ✓
4. D the confidence level ✓

Reject H0 when p-value

1. A exceeds α ✓
2. B is less than α (for the chosen test) ✓
3. C equals 1 always ✓
4. D equals the confidence level ✓

Power of a test is

1. A 1 − β, the probability of correctly rejecting a false H0 ✓
2. B the probability of Type I error ✓
3. C the p-value ✓
4. D the margin of error ✓

A two-tailed z-test for H0: μ = μ0 uses critical values

1. A ±z_{α/2} ✓
2. B z_α only on one side ✓
3. C t_{α/2} always ✓
4. D χ²_{α} ✓

One-sample z-test for mean is appropriate when

1. A σ is always unknown and n = 5 ✓
2. B σ is known and population is normal or n is large ✓
3. C population is always skewed with n = 10 ✓
4. D only for proportions ✓

One-sample t-test for mean is used when

1. A σ is known always ✓
2. B only for paired data ✓
3. C only for chi-square ✓
4. D σ is unknown, data are from normal population (or large n by robustness) ✓

Paired t-test analyzes

1. A two independent groups only ✓
2. B contingency tables only ✓
3. C differences within matched pairs ✓
4. D only proportions ✓

Two-sample t-test (independent) tests

1. A equality of two population means ✓
2. B equality of variances only always ✓
3. C only proportions ✓
4. D only goodness of fit ✓

Test statistic for two-sample z on proportions is

1. A t with n1+n2−2 always ✓
2. B z = (p̂1−p̂2)/SE(p̂1−p̂2) ✓
3. C χ² only ✓
4. D F only ✓

Critical region is

1. A always the middle of the distribution ✓
2. B the set of test statistic values leading to rejection of H0 ✓
3. C the confidence interval ✓
4. D the sample mean only ✓

Increasing sample size while effect size fixed generally

1. A increases power ✓
2. B increases β always ✓
3. C decreases power ✓
4. D leaves power unchanged always ✓

Decreasing α from 0.05 to 0.01

1. A increases power always ✓
2. B increases Type II error probability in many settings ✓
3. C reduces Type I error but lowers power ✓
4. D eliminates need for n ✓

Statistical significance at α = 0.05 means

1. A the effect is practically important ✓
2. B H0 is proven true ✓
3. C β = 0.05 ✓
4. D p-value < 0.05 under the conducted test ✓

Practical significance refers to

1. A only p < 0.05 ✓
2. B only Type I error ✓
3. C whether an effect is large enough to matter in context ✓
4. D only chi-square df ✓

A very small p-value suggests

1. A H0 is certainly true ✓
2. B the sample size is too small always ✓
3. C α should be raised ✓
4. D the observed data are unlikely if H0 were true ✓

Failing to reject H0

1. A does not prove H0 is true — may lack power ✓
2. B proves H0 is true ✓
3. C proves Ha is false ✓
4. D implies p = 1 ✓

One-sided test at α has

1. A α/2 in each tail ✓
2. B zero power ✓
3. C all α in one tail of the null distribution ✓
4. D no critical value ✓

Choosing one-sided vs two-sided test should be

1. A chosen after seeing direction of difference to maximize significance ✓
2. B always two-sided for proportions only ✓
3. C ignored in CSS exams ✓
4. D decided before seeing data based on research question ✓

z-test for H0: π = π0 uses

1. A t with n−1 ✓
2. B χ² with k−1 ✓
3. C only paired differences ✓
4. D z = (p̂−π0)/√[π0(1−π0)/n] ✓

Conditions for z-test on proportion include

1. A n = 1 always ✓
2. B normal population for each individual ✓
3. C np0 and n(1−p0) sufficiently large under H0 ✓
4. D equal variances ✓

Paired t-test df equal

1. A n1 + n2 − 2 ✓
2. B k − 1 ✓
3. C n − 1 where n is number of pairs ✓
4. D 2n ✓

The t-distribution has

1. A lighter tails always ✓
2. B heavier tails than the standard normal ✓
3. C no variance ✓
4. D df = 0 always ✓

As df → ∞, t-distribution approaches

1. A chi-square ✓
2. B F with 1 df ✓
3. C standard normal ✓
4. D uniform ✓

Test of H0: μ1 − μ2 = 0 with unequal variances uses

1. A pooled t always without checking ✓
2. B Welch's t-test with adjusted degrees of freedom ✓
3. C z with π0 ✓
4. D chi-square goodness of fit ✓

Pooled two-sample t-test assumes

1. A paired observations ✓
2. B multistage sampling only ✓
3. C only categorical data ✓
4. D equal population variances (σ1² = σ2²) ✓

F-test for equality of two variances is

1. A sensitive to non-normality — use with caution ✓
2. B always preferred to Levene test ✓
3. C identical to t-test on means ✓
4. D a chi-square test on means ✓

Levene's test assesses

1. A independence of proportions only ✓
2. B goodness of fit to Poisson ✓
3. C contingency independence only ✓
4. D homogeneity of variances without strong normality assumption ✓

Effect size for two means might use

1. A Cohen's d = (x̄1−x̄2)/sp ✓
2. B only p-value ✓
3. C only α ✓
4. D only chi-square statistic ✓

Bonferroni correction adjusts α when

1. A only one test is run ✓
2. B only for chi-square ✓
3. C sample size is infinite ✓
4. D multiple hypotheses are tested simultaneously ✓

A test statistic is standardized to compare

1. A only sample size ✓
2. B only confidence width ✓
3. C only non-sampling error ✓
4. D observed discrepancy from H0 to its null distribution ✓

Rejection rule for two-tailed t-test at α = 0.05

1. A t_obs > 0 only ✓
2. B |t_obs| < t_{0.025} ✓
3. C |t_obs| > t_{0.025, df} ✓
4. D use χ²_{0.05} ✓

If p-value = 0.03 at α = 0.05, decision is

1. A reject H0 ✓
2. B fail to reject H0 ✓
3. C accept H0 as proven ✓
4. D increase α to 0.01 ✓

If p-value = 0.08 at α = 0.05, decision is

1. A reject H0 ✓
2. B fail to reject H0 ✓
3. C prove Ha ✓
4. D set β = 0.08 ✓

Relationship between CI and two-sided test at α

1. A values inside (1−α)100% CI are not rejected as μ0 ✓
2. B CI always narrower than test region ✓
3. C unrelated procedures ✓
4. D CI replaces need for assumptions ✓

Robustness of t-test means

1. A never works without n > 10000 ✓
2. B moderate non-normality with adequate n often still valid ✓
3. C requires chi-square population ✓
4. D eliminates Type I error ✓

Nonparametric alternative to paired t when differences are non-normal

1. A z-test on proportions only ✓
2. B Wilcoxon signed-rank test ✓
3. C one-way ANOVA ✓
4. D chi-square independence ✓

Nonparametric alternative to two independent samples

1. A Mann–Whitney U (Wilcoxon rank-sum) test ✓
2. B paired t-test ✓
3. C goodness of fit only ✓
4. D F-test on means ✓

Hypothesis test requires

1. A assumptions about sampling, distribution, and independence ✓
2. B no assumptions if n > 5 ✓
3. C only graphical presentation ✓
4. D only census data ✓

One-tailed Ha: μ > μ0 rejects when

1. A test statistic is negative large ✓
2. B z or t exceeds positive critical value ✓
3. C p-value > α ✓
4. D χ² is small ✓

Standard error under H0 for one-sample mean z-test uses

1. A s/√n in denominator with H0 value in standardized form ✓
2. B π0(1−π0) ✓
3. C χ² df ✓
4. D σ/√n with μ0 in numerator setup ✓

Likelihood ratio test compares

1. A only sample means visually ✓
2. B only contingency margins ✓
3. C only index numbers ✓
4. D maximized likelihood under H0 vs unrestricted model ✓

α = 0.05 corresponds to

1. A 5% power ✓
2. B 5% Type I error if H0 is true and test assumptions hold ✓
3. C 95% Type II error always ✓
4. D 5% confidence coefficient ✓

β depends on

1. A only the p-value observed ✓
2. B only the confidence level ✓
3. C true parameter value, sample size, α, and effect size ✓
4. D only chi-square df alone ✓

A borderline p-value near α suggests

1. A definitive proof of H0 ✓
2. B inconclusive evidence — consider larger n or effect size ✓
3. C no need for replication ✓
4. D automatic rejection ✓

Testing H0: μ = 0 with t-test, the numerator of t is

1. A s only ✓
2. B σ² ✓
3. C p̂−π0 ✓
4. D x̄ − 0 ✓

For large samples, z and t critical values

1. A differ by factor of 2 always ✓
2. B t is always 0 ✓
3. C are nearly equal ✓
4. D z is always 3 ✓

False discovery rate control is important when

1. A only one t-test is performed ✓
2. B only descriptive stats are computed ✓
3. C many hypotheses are screened (multiple testing) ✓
4. D census is conducted ✓

Permutation test p-value is obtained by

1. A comparing observed statistic to distribution under random relabeling ✓
2. B using only z-tables always ✓
3. C assuming π = 0.5 always ✓
4. D ignoring the actual data ✓

Reporting only p-value without effect size

1. A is always best practice ✓
2. B eliminates Type II error ✓
3. C replaces assumptions check ✓
4. D can mislead when n is very large (tiny effects significant) ✓

In court analogy, Type I error is like

1. A freeing a guilty person ✓
2. B collecting evidence ✓
3. C convicting an innocent person ✓
4. D setting confidence level ✓

In court analogy, Type II error is like

1. A convicting innocent ✓
2. B announcing α ✓
3. C acquitting a guilty person ✓
4. D computing SE ✓

A significance test is not valid if

1. A n is large ✓
2. B α is 0.05 ✓
3. C t is used ✓
4. D data are not collected under a designed protocol (e.g., optional stopping without correction) ✓

Equivalence testing aims to show

1. A μ differs from μ0 by any amount ✓
2. B only p > 0.05 ✓
3. C parameter lies within a pre-specified practical equivalence margin ✓
4. D only chi-square fit ✓

Directional hypothesis after data peeking

1. A is always valid ✓
2. B inflates Type I error if not pre-specified ✓
3. C lowers α automatically ✓
4. D has no effect on inference ✓

The test statistic measures how many standard errors the sample estimate is from

1. A the confidence level ✓
2. B the chi-square df ✓
3. C the value specified under H0 ✓
4. D the population size N only ✓