TRB PG Assistant - Sample surveys - sampling frame, sampling with and without replacement, stratified sampling, two-stage, systematic and cluster sampling, regression and ratio estimates Question Bank with Options

1. Regression estimation uses auxiliary information to:

A) Increase the sample size.

B) Reduce the sampling variance by accounting for correlation.

C) Simplify the data collection process.

D) Eliminate non-sampling errors.

2. What is a common issue with cluster sampling if the clusters are not internally heterogeneous?

A) The sampling frame becomes too large.

B) The estimates may not be representative of the population.

C) The cost of data collection increases significantly.

D) Systematic bias is introduced.

3. If the sampling interval in a systematic sample is 'k', what does 'k' represent?

A) The number of strata.

B) The size of each cluster.

C) The ratio of population size to sample size.

D) The number of elements to skip between selections.

4. What is the main advantage of using a multi-stage sampling design?

A) It guarantees the highest possible precision.

B) It reduces the need for a complete sampling frame of individual elements.

C) It is always simpler to implement than single-stage designs.

D) It eliminates sampling bias.

5. In stratified sampling, the variance within strata is typically:

A) Higher than the variance between strata.

B) Lower than the variance between strata.

C) Equal to the variance between strata.

D) Irrelevant to the overall precision.

6. What is the defining feature of sampling without replacement?

A) Each selected unit is returned to the population before the next selection.

B) Once a unit is selected, it cannot be selected again.

C) The sampling frame is updated after each selection.

D) The probability of selection increases with each draw.

7. Which sampling technique is characterized by dividing the population into contiguous groups or 'clusters' that are geographically or organizationally defined?

A) Stratified Sampling

B) Systematic Sampling

C) Cluster Sampling

D) Simple Random Sampling

8. If a survey aims to estimate the total income of a city, and uses the number of registered vehicles as an auxiliary variable, what estimation method is likely to be employed?

A) Simple mean estimation

B) Ratio estimation

C) Stratified estimation

D) Systematic estimation

9. When is a regression estimate likely to provide a significant improvement in precision over a simple mean estimate?

A) When the auxiliary variable is not correlated with the study variable.

B) When the auxiliary variable is strongly correlated with the study variable.

C) When the population mean of the auxiliary variable is unknown.

D) When the sample size is very small.

10. What is the main drawback of cluster sampling compared to simple random sampling for the same number of elements?

A) It requires a more complex sampling frame.

B) It typically results in higher sampling errors.

C) It is more expensive to implement.

D) It is difficult to generalize findings to the population.

11. Systematic sampling with a random start is a method that aims to achieve:

A) Stratification of the population.

B) Homogeneity within clusters.

C) The properties of simple random sampling.

D) A reduction in the sampling frame size.

12. What is the term for the units selected in the second stage of a two-stage sampling design?

A) Primary Sampling Units (PSUs)

B) Secondary Sampling Units (SSUs)

C) Tertiary Sampling Units (TSUs)

D) Population Elements

13. In stratified sampling, the sampling within each stratum is typically done using:

A) Cluster Sampling

B) Systematic Sampling

C) Simple Random Sampling

D) Multi-stage Sampling

14. Sampling with replacement is theoretically simpler for probability calculations because:

A) The population size remains constant.

B) The sample size is always smaller than the population.

C) The probability of selecting any unit is always 1/N.

D) It avoids the need for a sampling frame.

15. What is a key advantage of using a sampling frame?

A) It eliminates sampling error.

B) It ensures that every unit in the population has a chance of being selected.

C) It reduces the cost of the survey.

D) It simplifies the analysis of the data.

16. Which estimate is generally preferred when the auxiliary variable is strongly correlated with the study variable and their relationship passes through the origin?

A) Simple mean estimator

B) Regression estimator

C) Ratio estimator

D) Stratified estimator

17. What is the core principle of regression estimation in surveys?

A) To use the average of the study variable.

B) To adjust the sample mean based on the known mean of an auxiliary variable and their relationship.

C) To simply sum up the values of the study variable.

D) To estimate the ratio of the study variable to the auxiliary variable.

18. In cluster sampling, if the clusters are selected randomly, what is assumed about the elements within the selected clusters?

A) They are internally homogeneous.

B) They are internally heterogeneous and representative of the population.

C) They are all identical.

D) They are selected through a secondary random process.

19. What is the primary risk associated with systematic sampling if the sampling frame has a periodic pattern?

A) Undercoverage of the population.

B) Overcoverage of the population.

C) Selection bias.

D) Increased sampling error.

20. When would a two-stage sampling design be most beneficial?

A) When the population is small and easily listed.

B) When the population is geographically dispersed and a complete frame is unavailable.

C) When high precision is required with a small sample size.

D) When all units are homogeneous.

21. In stratified sampling, if the researcher wants to ensure that small but important subgroups are adequately represented, what approach is taken?

A) Increase the sampling interval.

B) Allocate sample size disproportionately to strata.

C) Use cluster sampling within strata.

D) Perform sampling with replacement.

22. What happens to the sampling frame in sampling without replacement?

A) It is updated after each selection.

B) It remains static throughout the process.

C) It is discarded after the first selection.

D) It is expanded with new units.

23. Which sampling method ensures that every possible sample of a given size has an equal chance of being selected?

A) Systematic Sampling

B) Stratified Sampling

C) Cluster Sampling

D) Simple Random Sampling

24. The ratio estimator is a type of regression estimator where the regression line is assumed to pass through:

A) The point (0, mean of study variable).

B) The point (mean of auxiliary variable, 0).

C) The origin (0, 0).

D) The point (mean of auxiliary variable, mean of study variable).

25. Regression estimation is most effective when the correlation between the study variable and the auxiliary variable is:

A) Zero

B) Weak

C) Strong

D) Negative

26. What is a key challenge in cluster sampling?

A) Defining the strata.

B) Ensuring internal homogeneity within clusters.

C) Accounting for the variability between clusters.

D) Selecting the sampling interval.

27. Systematic sampling is often considered a practical alternative to simple random sampling because:

A) It guarantees better representation of the population.

B) It is easier to implement, especially with large populations.

C) It always leads to smaller sampling errors.

D) It does not require a sampling frame.

28. What is a primary sampling unit (PSU) in a multi-stage sampling design?

A) An individual element of the population.

B) The first set of groups selected from the population.

C) The final elements selected for the sample.

D) The entire population.

29. In stratified sampling, if the strata are defined based on income levels, what is the likely goal?

A) To simplify data collection.

B) To ensure representation of different income groups and potentially increase precision.

C) To reduce the sampling frame size.

D) To use systematic sampling within each stratum.

30. When is sampling without replacement preferred over sampling with replacement?

A) When the population size is very small.

B) When the cost of sampling is very high.

C) When the probability of selecting a unit should not change significantly.

D) When the population is infinite.

31. What is the term for the list of all units in the population from which a sample is to be selected?

A) Sampling frame

B) Sampling interval

C) Sampling stratum

D) Sampling cluster

32. Which sampling technique is most likely to be used for a national survey of households due to cost and logistical reasons?

A) Simple Random Sampling

B) Stratified Sampling

C) Systematic Sampling

D) Cluster Sampling

33. A ratio estimate is particularly useful when:

A) The auxiliary variable is not correlated with the study variable.

B) The relationship between the study variable and the auxiliary variable passes through the origin.

C) The population mean of the auxiliary variable is unknown.

D) The sampling frame is incomplete.

34. What is the primary assumption for the validity of a regression estimate?

A) The population mean of the auxiliary variable is unknown.

B) There is a linear relationship between the study variable and the auxiliary variable.

C) The sample size is very small.

D) The auxiliary variable is unrelated to the study variable.

35. In a two-stage sampling design, if the first-stage units are selected with equal probability, what is the implication for the second stage?

A) Second-stage units must also be selected with equal probability.

B) Second-stage units can be selected with unequal probabilities.

C) The second stage is not necessary.

D) The entire sample is selected in the first stage.

36. If a survey designer decides to select every 10th element from a randomly ordered list of the population, what sampling method is being used?

A) Stratified Sampling

B) Cluster Sampling

C) Systematic Sampling

D) Simple Random Sampling

37. What is a potential disadvantage of cluster sampling?

A) It requires a complete list of all population elements.

B) It can lead to higher sampling errors if clusters are not representative.

C) It is computationally intensive.

D) It is difficult to implement in practice.

38. In stratified sampling, if the strata are internally homogeneous and externally heterogeneous, what is the benefit?

A) It simplifies the sampling process.

B) It leads to more precise estimates compared to SRS.

C) It requires a smaller sampling frame.

D) It reduces the cost of data collection.

39. Which of the following statements is true for sampling without replacement?

A) The probability of selecting a unit changes after it is selected.

B) The selected unit is returned to the population before the next selection.

C) It is generally less efficient than sampling with replacement.

D) It always results in a larger sample size.

40. What is the main idea behind a ratio estimate in sample surveys?

A) To use the ratio of the study variable to an auxiliary variable.

B) To estimate the ratio of two study variables.

C) To reduce the variance of the estimate.

D) To incorporate auxiliary information in a specific way.

41. A regression estimate uses the relationship between the study variable and what other type of variable?

A) A dependent variable

B) An auxiliary variable

C) A confounding variable

D) A response variable

42. What is the primary goal of a regression estimate in sample surveys?

A) To increase the sample size.

B) To improve the precision of estimates by using auxiliary information.

C) To reduce the cost of the survey.

D) To simplify data collection.

43. Which sampling method is often used when the population is geographically dispersed?

A) Stratified Sampling

B) Systematic Sampling

C) Cluster Sampling

D) Simple Random Sampling

44. In cluster sampling, the population is divided into groups called clusters. What is a typical characteristic of these clusters?

A) They are internally homogeneous.

B) They are internally heterogeneous.

C) They are usually small in size.

D) They are drawn randomly without any structure.

45. What is a key characteristic of systematic sampling?

A) Every unit has an equal chance of being selected.

B) The sampling interval is used to select units.

C) It requires dividing the population into strata.

D) It involves selecting groups of units.

46. In a two-stage sampling design, what is selected in the first stage?

A) Individual elements of the population.

B) Primary sampling units (PSUs).

C) Secondary sampling units (SSUs).

D) The entire sample.

47. What is the main advantage of stratified sampling over simple random sampling?

A) It is simpler to implement.

B) It can provide more precise estimates for the same sample size.

C) It does not require a sampling frame.

D) It is less prone to sampling errors.

48. Which sampling method involves dividing the population into homogeneous subgroups called strata?

A) Simple Random Sampling

B) Systematic Sampling

C) Stratified Sampling

D) Cluster Sampling

49. In sampling with replacement, what happens to the probability of selecting a unit after it has been chosen?

A) It decreases.

B) It increases.

C) It remains the same.

D) It becomes zero.

50. What is the primary purpose of a sampling frame in a sample survey?

A) To define the population of interest.

B) To provide a list of all units from which the sample will be drawn.

C) To determine the sample size.

D) To analyze the collected data.

Sample surveys - sampling frame, sampling with and without replacement, stratified sampling, two-stage, systematic and cluster sampling, regression and ratio estimates - Question Bank