Sampling and Sampling Distributions MCQs 2026

Simple random sampling (SRS) means

1. A only the first n units are taken ✓
2. B units are chosen by judgment of the interviewer ✓
3. C every possible sample of size n has an equal chance of selection ✓
4. D only clusters are selected ✓

A sampling frame is

1. A the final sample only ✓
2. B the list or map of population units from which the sample is drawn ✓
3. C the confidence interval formula ✓
4. D the p-value of a test ✓

Sampling error refers to

1. A mistakes in data entry only ✓
2. B bias from a poorly designed questionnaire only ✓
3. C errors in copying tables ✓
4. D the discrepancy between a sample statistic and the population parameter due to random selection ✓

Non-sampling error includes

1. A only random variation from SRS ✓
2. B only the standard error of the mean ✓
3. C only Type I error ✓
4. D coverage error, nonresponse and measurement error ✓

In stratified sampling, the population is

1. A divided into clusters selected at random ✓
2. B divided into homogeneous strata and samples are drawn from each stratum ✓
3. C sampled without any structure ✓
4. D always sampled one unit at a time from a sorted list ✓

Proportional stratified sampling draws from each stratum

1. A with equal numbers regardless of size ✓
2. B in proportion to stratum size in the population ✓
3. C only from the largest stratum ✓
4. D without replacement from other strata ✓

Optimum allocation in stratified sampling minimizes variance by

1. A taking equal n from every stratum always ✓
2. B ignoring within-stratum variance ✓
3. C sampling only one stratum ✓
4. D allocating more sample to strata with larger size and greater variability ✓

Systematic sampling selects every k-th unit after

1. A always starting at unit 1 ✓
2. B a random start between 1 and k ✓
3. C sorting by the variable of interest only ✓
4. D selecting clusters first ✓

The sampling interval k in systematic sampling equals

1. A n divided by N ✓
2. B the standard deviation ✓
3. C population size N divided by sample size n ✓
4. D the confidence level ✓

Systematic sampling can resemble SRS when

1. A the frame order is unrelated to the study variable ✓
2. B the list is perfectly periodic with period k ✓
3. C only judgment is used ✓
4. D clusters overlap ✓

Cluster sampling selects

1. A individual units with equal probability ignoring groups ✓
2. B only the largest units in the population ✓
3. C strata with optimum allocation only ✓
4. D groups (clusters) of units and often surveys all or a subsample within chosen clusters ✓

Cluster sampling is often

1. A always more precise than stratified sampling ✓
2. B free of design effects ✓
3. C more economical but usually less precise than SRS for the same total sample size ✓
4. D identical to systematic sampling ✓

In single-stage cluster sampling

1. A all units in selected clusters are measured ✓
2. B only one unit per cluster is ever taken ✓
3. C strata are formed within clusters first ✓
4. D two frames are merged ✓

Multistage sampling involves

1. A selecting primary units, then subsampling within them in successive stages ✓
2. B drawing a single SRS in one step only ✓
3. C non-probability convenience selection ✓
4. D sorting and taking every k-th unit only ✓

A two-stage cluster design might first select

1. A strata and then ignore clusters ✓
2. B primary sampling units (PSUs) and then sample households within PSUs ✓
3. C every individual directly by SRS ✓
4. D only the last stage without a frame ✓

Probability sampling requires

1. A only convenience access ✓
2. B judgment of the enumerator ✓
3. C known nonzero selection probabilities for each unit ✓
4. D volunteer participation ✓

Non-probability sampling includes

1. A simple random sampling ✓
2. B stratified random sampling ✓
3. C multistage probability sampling ✓
4. D convenience, quota and purposive sampling ✓

The parameter is

1. A a value calculated from sample data only ✓
2. B a numerical characteristic of the population ✓
3. C always the sample mean ✓
4. D the significance level alpha ✓

The sampling distribution of a statistic is

1. A the probability distribution of the statistic over all possible samples ✓
2. B the histogram of one sample only ✓
3. C the population distribution itself ✓
4. D the confidence interval width ✓

The standard error of the sample mean equals

1. A σ/√n when sampling from an infinite population with replacement or negligible finite correction ✓
2. B σ·n ✓
3. C σ²·n ✓
4. D √(σ/n) ✓

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

1. A the chi-square with n df ✓
2. B the F distribution always ✓
3. C the uniform distribution ✓
4. D Student's t with n−1 degrees of freedom (assuming normal population) ✓

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

1. A normal regardless of population shape (under finite variance) ✓
2. B always uniform ✓
3. C always identical to the population distribution ✓
4. D chi-square ✓

The Central Limit Theorem requires

1. A independent observations and a sufficiently large sample size (with finite variance) ✓
2. B a perfectly normal population only ✓
3. C n = 2 always ✓
4. D zero sampling error ✓

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

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

The sampling distribution of p̂ is approximately normal when

1. A n is always 2 ✓
2. B p equals zero only ✓
3. C np and n(1−p) are both sufficiently large (rule of thumb ≥5 or 10) ✓
4. D the population is finite only ✓

Finite population correction (FPC) factor is

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

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

1. A units become independent ✓
2. B σ becomes zero ✓
3. C n increases automatically ✓
4. D selection of one unit alters probabilities for remaining units (negative dependence) ✓

Design effect (DEFF) measures

1. A the ratio of variance under a complex design to variance under SRS with same n ✓
2. B only nonresponse rate ✓
3. C only coverage error ✓
4. D the p-value ✓

Self-weighting sample design means

1. A weights vary greatly ✓
2. B each selected unit represents the same number of population units ✓
3. C only cluster sampling is used ✓
4. D strata are ignored ✓

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

1. A always larger than any other design ✓
2. B smaller than SRS variance when strata are homogeneous internally ✓
3. C zero always ✓
4. D unaffected by stratum choice ✓

Judgment (purposive) sampling is

1. A equivalent to SRS ✓
2. B the same as systematic sampling with random start ✓
3. C non-probability selection based on researcher judgment ✓
4. D optimum allocation ✓

Quota sampling resembles stratified sampling but

1. A uses known selection probabilities ✓
2. B always equals SRS ✓
3. C eliminates non-sampling error ✓
4. D does not assign random selection within quotas ✓

Snowball sampling is used when

1. A hard-to-reach populations are located through referrals ✓
2. B complete frames exist ✓
3. C SRS is cheapest ✓
4. D clusters are identical ✓

Bootstrap resampling draws

1. A repeated samples with replacement from the observed sample to estimate sampling variation ✓
2. B only from the population frame ✓
3. C without replacement from the population only ✓
4. D chi-square tables ✓

The mean of the sampling distribution of x̄ equals

1. A the population mean μ ✓
2. B zero always ✓
3. C s/√n ✓
4. D the sample median ✓

The variance of x̄ under SRS from an infinite population is

1. A σ/√n ✓
2. B σ·n ✓
3. C σ²·√n ✓
4. D σ²/n ✓

Increasing sample size n while holding σ fixed

1. A increases SE ✓
2. B decreases the standard error of the mean ✓
3. C leaves SE unchanged ✓
4. D makes SE equal σ ✓

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

1. A only when n > 1000 ✓
2. B for any sample size n ✓
3. C never ✓
4. D only when σ is unknown ✓

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

1. A chi-square with n1+n2 df ✓
2. B t with n1 df only ✓
3. C normal with mean μ1−μ2 and variance σ1²/n1 + σ2²/n2 ✓
4. D always zero ✓

PPS (probability proportional to size) sampling gives

1. A every unit equal chance regardless of size ✓
2. B zero probability to large units ✓
3. C larger units higher selection probability ✓
4. D only systematic selection ✓

Primary sampling units (PSUs) in multistage surveys are often

1. A always individual persons only ✓
2. B only the last-stage elements ✓
3. C the sampling frame of strata labels ✓
4. D geographic areas such as blocks or villages ✓

Coverage error occurs when

1. A only random sampling variation occurs ✓
2. B some population units are missing from the sampling frame ✓
3. C every unit has equal weight ✓
4. D the sample size is large ✓

Response rate affects

1. A only sampling error under SRS ✓
2. B the definition of parameter ✓
3. C the CLT requirement only ✓
4. D nonresponse bias if respondents differ from nonrespondents ✓

Replication (rerandomization) in survey research helps assess

1. A population normality only ✓
2. B chi-square df ✓
3. C Type I error only ✓
4. D stability of estimates under the sampling design ✓

In cluster sampling, effective sample size is often

1. A larger than nominal n always ✓
2. B equal to number of clusters times 1 always ✓
3. C smaller than the nominal n due to intra-cluster correlation ✓
4. D infinite ✓

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

1. A zero ✓
2. B 1−π always ✓
3. C the population proportion π ✓
4. D π(1−π) ✓

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

1. A always normal ✓
2. B always degenerate at zero ✓
3. C chi-square ✓
4. D the same as the population distribution ✓

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

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

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

1. A a smaller finite population always ✓
2. B an infinite population when estimating variance of x̄ (no FPC) ✓
3. C a stratified population only ✓
4. D a chi-square population ✓

A census differs from a sample survey because a census

1. A always has larger sampling error ✓
2. B uses only cluster sampling ✓
3. C never has non-sampling error ✓
4. D attempts to measure every population unit ✓

Pilot survey before main survey helps

1. A test instruments and estimate variances for sample size planning ✓
2. B eliminate all bias ✓
3. C replace probability sampling ✓
4. D avoid the need for a frame ✓

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

1. A that of SRS when no periodicity exists ✓
2. B always zero ✓
3. C always larger than cluster sampling ✓
4. D unaffected by order ✓

The law of large numbers supports sampling because

1. A sample variance converges to zero instantly for any n ✓
2. B parameters become statistics ✓
3. C sample averages converge to population mean as n increases ✓
4. D Type II error vanishes ✓

Transforming sampling weights to sum to sample size is called

1. A normalization of weights ✓
2. B stratification ✓
3. C bootstrapping ✓
4. D randomization ✓

Horvitz–Thompson estimator uses

1. A only convenience weights ✓
2. B inclusion probabilities to form unbiased population total estimates ✓
3. C only chi-square tests ✓
4. D only cluster means without weights ✓

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

1. A Var(x̄) = 0 ✓
2. B x̄ always equals μ ✓
3. C E(x̄) = μ ✓
4. D n must equal N ✓

Sampling fraction f = n/N approaching 1 implies

1. A SE increases without bound ✓
2. B CLT fails always ✓
3. C FPC substantially reduces standard errors ✓
4. D stratification is impossible ✓

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

1. A always Poisson ✓
2. B always uniform ✓
3. C normal by CLT when individual values have finite variance ✓
4. D exactly t with n−1 df ✓

Random digit table or RNG in SRS ensures

1. A periodic bias in every list ✓
2. B zero sampling error ✓
3. C complete elimination of nonresponse ✓
4. D selection without subjective bias ✓