Sample Survey Scope and Representativeness Explained

This question requires us to evaluate two statements, labeled Assertion A and Reason R, concerning sample surveys. We need to determine the validity of each statement and ascertain if Reason R correctly explains Assertion A.

Assertion A Analysis: Scope of Sample Surveys

Assertion A states: "A sample survey is usually extensive in scope."

In the field of research methodology, the "scope" of a survey refers to the range and depth of topics it covers. While a sample survey, by definition, collects data from a subset of a population rather than the entire population (as in a census), it can still be "extensive". This extensiveness typically refers to the breadth of information collected across various characteristics, variables, or aspects relevant to the research question. It implies a comprehensive examination of the chosen sample concerning multiple factors, allowing for detailed analysis.

Reason R Analysis: Representativeness Requirement

Reason R states: "Therefore, both in the number of cases included and in the manner of their selection, it has to be adequately and faithfully representative of a larger population."

This statement outlines a crucial requirement for any valid sample survey. For the findings derived from a sample to be reliably generalized to the broader population from which the sample was drawn, the sample must be representative. This involves two key elements:

• Adequate Number of Cases: The sample size must be sufficient to ensure statistical significance and minimize the margin of error. A too-small sample might not capture the population's diversity accurately.
• Faithful Selection Method: The procedure used to select the sample members must be unbiased. Techniques like random sampling are employed to ensure that each member of the population has a non-zero (and often known) probability of being selected, thus preventing systematic bias.

Representativeness is the foundation upon which the inferences drawn from a sample survey are built.

Linking Assertion and Reason: Why R Explains A

Reason R serves as a logical explanation for Assertion A. The need for a sample survey to be representative (as stated in R) directly influences and enables its extensive scope (as stated in A).

Because a sample must accurately reflect the characteristics of the entire population to yield valid conclusions, researchers must design the survey instrument and sampling strategy meticulously. This often means including questions covering a wide array of relevant variables and ensuring the sampling method captures the heterogeneity of the population. Therefore, the commitment to achieving representativeness (R) necessitates that the survey possesses an extensive scope (A) in terms of the data it collects and the population characteristics it aims to describe.

Evaluating the Options

Based on the analysis of Assertion A and Reason R:

• Both Assertion A ("A sample survey is usually extensive in scope") and Reason R ("it has to be adequately and faithfully representative...") are factually correct statements in the context of survey methodology.
• Reason R provides the underlying principle (representativeness) that explains why and how a sample survey achieves its extensive scope. The careful selection and adequate sizing needed for representativeness allow the survey to cover many aspects of the population extensively.

Therefore, the option stating that both A and R are correct and R is the correct explanation of A is the most appropriate choice.