Sampling and Sampling Distributions MCQs 2026

Simple random sampling (SRS) means

1. Aonly the first n units are taken✓
2. Bunits are chosen by judgment of the interviewer✓
3. Cevery possible sample of size n has an equal chance of selection✓
4. Donly clusters are selected✓

Random digit table or RNG in SRS ensures

1. Aperiodic bias in every list✓
2. Bzero sampling error✓
3. Ccomplete elimination of nonresponse✓
4. Dselection without subjective bias✓

Distribution of sample total ΣXi under SRS (large n) is approximately

1. Aalways Poisson✓
2. Balways uniform✓
3. Cnormal by CLT when individual values have finite variance✓
4. Dexactly t with n−1 df✓

Sampling fraction f = n/N approaching 1 implies

1. ASE increases without bound✓
2. BCLT fails always✓
3. CFPC substantially reduces standard errors✓
4. Dstratification is impossible✓

Under SRS, the sample mean is an unbiased estimator of μ because

1. AVar(x̄) = 0✓
2. Bx̄ always equals μ✓
3. CE(x̄) = μ✓
4. Dn must equal N✓

Horvitz–Thompson estimator uses

1. Aonly convenience weights✓
2. Binclusion probabilities to form unbiased population total estimates✓
3. Conly chi-square tests✓
4. Donly cluster means without weights✓

Transforming sampling weights to sum to sample size is called

1. Anormalization of weights✓
2. Bstratification✓
3. Cbootstrapping✓
4. Drandomization✓

The law of large numbers supports sampling because

1. Asample variance converges to zero instantly for any n✓
2. Bparameters become statistics✓
3. Csample averages converge to population mean as n increases✓
4. DType II error vanishes✓

In systematic sampling from a random-ordered list of N units, variance of the mean estimator is approximately

1. Athat of SRS when no periodicity exists✓
2. Balways zero✓
3. Calways larger than cluster sampling✓
4. Dunaffected by order✓

Pilot survey before main survey helps

1. Atest instruments and estimate variances for sample size planning✓
2. Beliminate all bias✓
3. Creplace probability sampling✓
4. Davoid the need for a frame✓

A census differs from a sample survey because a census

1. Aalways has larger sampling error✓
2. Buses only cluster sampling✓
3. Cnever has non-sampling error✓
4. Dattempts to measure every population unit✓

Sampling with replacement from a finite population of size N is equivalent to sampling from

1. Aa smaller finite population always✓
2. Ban infinite population when estimating variance of x̄ (no FPC)✓
3. Ca stratified population only✓
4. Da chi-square population✓

The standard error of the difference p̂1−p̂2 (independent large samples) is approximately

1. Ap̂1−p̂2✓
2. B√[p̂1(1−p̂1)/n1 + p̂2(1−p̂2)/n2]✓
3. C√(n1+n2)✓
4. Dp̂1/n1 only✓

When n = 1 in SRS, the sampling distribution of x̄ is

1. Aalways normal✓
2. Balways degenerate at zero✓
3. Cchi-square✓
4. Dthe same as the population distribution✓

Linear on the sampling distribution of a proportion, the mean of p̂ equals

1. Azero✓
2. B1−π always✓
3. Cthe population proportion π✓
4. Dπ(1−π)✓

In cluster sampling, effective sample size is often

1. Alarger than nominal n always✓
2. Bequal to number of clusters times 1 always✓
3. Csmaller than the nominal n due to intra-cluster correlation✓
4. Dinfinite✓

Replication (rerandomization) in survey research helps assess

1. Apopulation normality only✓
2. Bchi-square df✓
3. CType I error only✓
4. Dstability of estimates under the sampling design✓

Response rate affects

1. Aonly sampling error under SRS✓
2. Bthe definition of parameter✓
3. Cthe CLT requirement only✓
4. Dnonresponse bias if respondents differ from nonrespondents✓

Coverage error occurs when

1. Aonly random sampling variation occurs✓
2. Bsome population units are missing from the sampling frame✓
3. Cevery unit has equal weight✓
4. Dthe sample size is large✓

Primary sampling units (PSUs) in multistage surveys are often

1. Aalways individual persons only✓
2. Bonly the last-stage elements✓
3. Cthe sampling frame of strata labels✓
4. Dgeographic areas such as blocks or villages✓

PPS (probability proportional to size) sampling gives

1. Aevery unit equal chance regardless of size✓
2. Bzero probability to large units✓
3. Clarger units higher selection probability✓
4. Donly systematic selection✓

The sampling distribution of the difference of two independent sample means (equal variances, large n) is approximately

1. Achi-square with n1+n2 df✓
2. Bt with n1 df only✓
3. Cnormal with mean μ1−μ2 and variance σ1²/n1 + σ2²/n2✓
4. Dalways zero✓

If population distribution is normal, the sampling distribution of x̄ is normal

1. Aonly when n > 1000✓
2. Bfor any sample size n✓
3. Cnever✓
4. Donly when σ is unknown✓

Increasing sample size n while holding σ fixed

1. Aincreases SE✓
2. Bdecreases the standard error of the mean✓
3. Cleaves SE unchanged✓
4. Dmakes SE equal σ✓

The variance of x̄ under SRS from an infinite population is

1. Aσ/√n✓
2. Bσ·n✓
3. Cσ²·√n✓
4. Dσ²/n✓

The mean of the sampling distribution of x̄ equals

1. Athe population mean μ✓
2. Bzero always✓
3. Cs/√n✓
4. Dthe sample median✓

Bootstrap resampling draws

1. Arepeated samples with replacement from the observed sample to estimate sampling variation✓
2. Bonly from the population frame✓
3. Cwithout replacement from the population only✓
4. Dchi-square tables✓

Snowball sampling is used when

1. Ahard-to-reach populations are located through referrals✓
2. Bcomplete frames exist✓
3. CSRS is cheapest✓
4. Dclusters are identical✓

Quota sampling resembles stratified sampling but

1. Auses known selection probabilities✓
2. Balways equals SRS✓
3. Celiminates non-sampling error✓
4. Ddoes not assign random selection within quotas✓

Judgment (purposive) sampling is

1. Aequivalent to SRS✓
2. Bthe same as systematic sampling with random start✓
3. Cnon-probability selection based on researcher judgment✓
4. Doptimum allocation✓

In stratified sampling, variance of the overall mean estimator can be

1. Aalways larger than any other design✓
2. Bsmaller than SRS variance when strata are homogeneous internally✓
3. Czero always✓
4. Dunaffected by stratum choice✓

Self-weighting sample design means

1. Aweights vary greatly✓
2. Beach selected unit represents the same number of population units✓
3. Conly cluster sampling is used✓
4. Dstrata are ignored✓

Design effect (DEFF) measures

1. Athe ratio of variance under a complex design to variance under SRS with same n✓
2. Bonly nonresponse rate✓
3. Conly coverage error✓
4. Dthe p-value✓

Without replacement from a finite population, variance of x̄ is smaller than with replacement because

1. Aunits become independent✓
2. Bσ becomes zero✓
3. Cn increases automatically✓
4. Dselection of one unit alters probabilities for remaining units (negative dependence)✓

Finite population correction (FPC) factor is

1. A√[(N−n)/(N−1)] multiplying the standard error when sampling without replacement from finite N✓
2. Bn/N only✓
3. CN/n✓
4. Dalways 1 regardless of N✓

The sampling distribution of p̂ is approximately normal when

1. An is always 2✓
2. Bp equals zero only✓
3. Cnp and n(1−p) are both sufficiently large (rule of thumb ≥5 or 10)✓
4. Dthe population is finite only✓

For a sample proportion p̂, the standard error (infinite population) is approximately

1. Ap/n✓
2. B√(np)✓
3. C√[p(1−p)/n]✓
4. D1−p only✓

The Central Limit Theorem requires

1. Aindependent observations and a sufficiently large sample size (with finite variance)✓
2. Ba perfectly normal population only✓
3. Cn = 2 always✓
4. Dzero sampling error✓

For large n, by the Central Limit Theorem, the sampling distribution of x̄ is approximately

1. Anormal regardless of population shape (under finite variance)✓
2. Balways uniform✓
3. Calways identical to the population distribution✓
4. Dchi-square✓

If population standard deviation σ is unknown and n is small, the sampling distribution of x̄ is often modeled by

1. Athe chi-square with n df✓
2. Bthe F distribution always✓
3. Cthe uniform distribution✓
4. DStudent's t with n−1 degrees of freedom (assuming normal population)✓

The standard error of the sample mean equals

1. Aσ/√n when sampling from an infinite population with replacement or negligible finite correction✓
2. Bσ·n✓
3. Cσ²·n✓
4. D√(σ/n)✓

The sampling distribution of a statistic is

1. Athe probability distribution of the statistic over all possible samples✓
2. Bthe histogram of one sample only✓
3. Cthe population distribution itself✓
4. Dthe confidence interval width✓

The parameter is

1. Aa value calculated from sample data only✓
2. Ba numerical characteristic of the population✓
3. Calways the sample mean✓
4. Dthe significance level alpha✓

Non-probability sampling includes

1. Asimple random sampling✓
2. Bstratified random sampling✓
3. Cmultistage probability sampling✓
4. Dconvenience, quota and purposive sampling✓

Probability sampling requires

1. Aonly convenience access✓
2. Bjudgment of the enumerator✓
3. Cknown nonzero selection probabilities for each unit✓
4. Dvolunteer participation✓

A two-stage cluster design might first select

1. Astrata and then ignore clusters✓
2. Bprimary sampling units (PSUs) and then sample households within PSUs✓
3. Cevery individual directly by SRS✓
4. Donly the last stage without a frame✓

Multistage sampling involves

1. Aselecting primary units, then subsampling within them in successive stages✓
2. Bdrawing a single SRS in one step only✓
3. Cnon-probability convenience selection✓
4. Dsorting and taking every k-th unit only✓

In single-stage cluster sampling

1. Aall units in selected clusters are measured✓
2. Bonly one unit per cluster is ever taken✓
3. Cstrata are formed within clusters first✓
4. Dtwo frames are merged✓

Cluster sampling is often

1. Aalways more precise than stratified sampling✓
2. Bfree of design effects✓
3. Cmore economical but usually less precise than SRS for the same total sample size✓
4. Didentical to systematic sampling✓

Cluster sampling selects

1. Aindividual units with equal probability ignoring groups✓
2. Bonly the largest units in the population✓
3. Cstrata with optimum allocation only✓
4. Dgroups (clusters) of units and often surveys all or a subsample within chosen clusters✓

Systematic sampling can resemble SRS when

1. Athe frame order is unrelated to the study variable✓
2. Bthe list is perfectly periodic with period k✓
3. Conly judgment is used✓
4. Dclusters overlap✓

The sampling interval k in systematic sampling equals

1. An divided by N✓
2. Bthe standard deviation✓
3. Cpopulation size N divided by sample size n✓
4. Dthe confidence level✓

Systematic sampling selects every k-th unit after

1. Aalways starting at unit 1✓
2. Ba random start between 1 and k✓
3. Csorting by the variable of interest only✓
4. Dselecting clusters first✓

Optimum allocation in stratified sampling minimizes variance by

1. Ataking equal n from every stratum always✓
2. Bignoring within-stratum variance✓
3. Csampling only one stratum✓
4. Dallocating more sample to strata with larger size and greater variability✓

Proportional stratified sampling draws from each stratum

1. Awith equal numbers regardless of size✓
2. Bin proportion to stratum size in the population✓
3. Conly from the largest stratum✓
4. Dwithout replacement from other strata✓

In stratified sampling, the population is

1. Adivided into clusters selected at random✓
2. Bdivided into homogeneous strata and samples are drawn from each stratum✓
3. Csampled without any structure✓
4. Dalways sampled one unit at a time from a sorted list✓

Non-sampling error includes

1. Aonly random variation from SRS✓
2. Bonly the standard error of the mean✓
3. Conly Type I error✓
4. Dcoverage error, nonresponse and measurement error✓

Sampling error refers to

1. Amistakes in data entry only✓
2. Bbias from a poorly designed questionnaire only✓
3. Cerrors in copying tables✓
4. Dthe discrepancy between a sample statistic and the population parameter due to random selection✓

A sampling frame is

1. Athe final sample only✓
2. Bthe list or map of population units from which the sample is drawn✓
3. Cthe confidence interval formula✓
4. Dthe p-value of a test✓