Sampling Theory
40 questions across 3 topics. Also examined in CNET, ISS.
Simple Random, Stratified and Systematic Sampling
- 163Sample size for a specified margin of errorMSET June 2025Simple Random, Stratified and Systematic SamplingHard
- 165The Horvitz–Thompson estimatorMSET June 2025Simple Random, Stratified and Systematic SamplingHard
- 166Post-stratification versus proportional allocationMSET June 2025Simple Random, Stratified and Systematic SamplingHard
- 163Sampling theory — spotting a formula with a missing factorMSET April 2024Simple Random, Stratified and Systematic SamplingHard
- 167Systematic sampling — decomposing total variabilityMSET April 2024Simple Random, Stratified and Systematic SamplingMedium
- 163Systematic sampling — equal selection probability, without a guaranteed efficiency edgeMSET March 2023Simple Random, Stratified and Systematic SamplingHard
- 165The standard inclusion-probability bound for Midzuno's designMSET March 2023Simple Random, Stratified and Systematic SamplingEasy
- 166Post-stratification — stratifying after the factMSET March 2023Simple Random, Stratified and Systematic SamplingEasy
- 126A mixed unequal-probability/SRSWOR design — the sample mean is biased, but an unbiased estimator still existsMSET September 2021Simple Random, Stratified and Systematic SamplingHard
- 127Regression estimator versus sample mean — an asymptotic, not universal, comparisonMSET September 2021Simple Random, Stratified and Systematic SamplingHard
- 166Inclusion probability under a two-stage unequal-then-equal designMSET September 2021Simple Random, Stratified and Systematic SamplingHard
- 168Variance of a sample proportion under SRSWORMSET September 2021Simple Random, Stratified and Systematic SamplingEasy
- 126A mixed selection mechanism gives multiples of k two routes into the sample, breaking equal inclusion probabilityMSET December 2020Simple Random, Stratified and Systematic SamplingHard
- 127Systematic sampling is efficient precisely when the population carries a linear trendMSET December 2020Simple Random, Stratified and Systematic SamplingHard
- 166Only one of the two possible systematic samples contains both unitsMSET December 2020Simple Random, Stratified and Systematic SamplingEasy
- 168Post-stratification approaches full stratification's efficiency when strata are well-filledMSET December 2020Simple Random, Stratified and Systematic SamplingHard
- 126Random halving, then one unit per half, gives every pair the same chanceMSET June 2019Simple Random, Stratified and Systematic SamplingMedium
- 127Proportional allocation never does worse than SRSWOR of the same sizeMSET June 2019Simple Random, Stratified and Systematic SamplingEasy
- 81With rhowsy=0, systematic sampling has the SRSWR varianceMSET January 2018 Paper IISimple Random, Stratified and Systematic SamplingMedium
- 82Inclusion probability under SRSWOR: binomN-1n-1/binom Nn=n/NMSET January 2018 Paper IISimple Random, Stratified and Systematic SamplingEasy
- 123Cluster sampling loses to SRSWOR exactly when (M-1)rho0MSET January 2018 Paper IIISimple Random, Stratified and Systematic SamplingMedium
- 81Equal-width strata of a uniform cut the variance by the factor 1/L^2MSET April 2017 Paper IISimple Random, Stratified and Systematic SamplingMedium
- 82Cluster sampling is usually the least efficient per elementMSET April 2017 Paper IISimple Random, Stratified and Systematic SamplingEasy
- 122Clusters of size one are just unitsMSET April 2017 Paper IIISimple Random, Stratified and Systematic SamplingMedium
Ratio and Regression Methods
- 165Ratio estimation — from a size-2 SRSWOR sampleMSET April 2024Ratio and Regression MethodsMedium
- 167Double sampling — filling a gap in auxiliary-variable coverageMSET March 2023Ratio and Regression MethodsMedium
- 167Regression estimator's efficiency edge is an asymptotic guaranteeMSET September 2021Ratio and Regression MethodsMedium
- 167Bias of the ratio estimator from Cov(r,bar x)=bar Y-bar X,E(r)MSET June 2019Ratio and Regression MethodsMedium
- 168Regression beats both, but mean versus ratio depends on rhoMSET June 2019Ratio and Regression MethodsMedium
- 121The exact bias of the regression estimator is -Cov(b,bar x)MSET January 2018 Paper IIIRatio and Regression MethodsMedium
- 122The ratio estimator's bias is O(1/n)MSET January 2018 Paper IIIRatio and Regression MethodsEasy
- 119The ratio estimator wins when rhofrac12,CV(x)/CV(y)MSET April 2017 Paper IIIRatio and Regression MethodsEasy
- 120Regression gains rho^2; with rho=0 it gains nothingMSET April 2017 Paper IIIRatio and Regression MethodsEasy
Probability Proportional to Size Sampling
- 164PPSWOR — probability at the third drawMSET June 2025Probability Proportional to Size SamplingHard
- 164Computing inclusion probabilities from an explicit sampling designMSET March 2023Probability Proportional to Size SamplingMedium
- 166Inclusion probability under successive PPS draws: z3+sumine3ziz3/(1-zi)MSET June 2019Probability Proportional to Size SamplingMedium
- 124For a fixed-size design, sumjne ipiij=(n-1)piiMSET January 2018 Paper IIIProbability Proportional to Size SamplingMedium
- 125Equal selection probabilities turn PPSWR into SRSWRMSET January 2018 Paper IIIProbability Proportional to Size SamplingEasy
- 121Fixed sample size: sumpii=nMSET April 2017 Paper IIIProbability Proportional to Size SamplingEasy
- 123With replacement, every draw uses the same probabilities piMSET April 2017 Paper IIIProbability Proportional to Size SamplingEasy