Analysis of Assertion (A)

The assertion states that stratified sampling relies on simple random sampling and uses methods to boost representativeness.

• Stratified sampling involves dividing a population into distinct subgroups (strata).
• Simple random sampling (SRS) is typically employed within each stratum to select participants.
• The primary aim of stratified sampling is to ensure that subgroups are represented in the sample proportionally to their size in the population, thereby increasing the sample's overall representativeness, especially in diverse populations.

Therefore, Assertion (A) is considered correct.

Analysis of Reason (R)

The reason claims that a homogenous population requires a smaller sample size compared to a heterogenous one.

• A homogenous population has members with similar characteristics, leading to less variability.
• A heterogenous population has members with diverse characteristics, resulting in higher variability.
• To accurately capture the variability within a population, a larger sample size is generally needed for more diverse (heterogenous) populations. Conversely, a more uniform (homogenous) population requires a smaller sample size to achieve similar precision.

Therefore, Reason (R) is considered correct.

Relationship Between Assertion (A) and Reason (R)

The question asks if Reason (R) correctly explains Assertion (A).

• Assertion (A) describes the methodology and goal of stratified sampling.
• Reason (R) explains the relationship between population homogeneity/heterogeneity and sample size requirements.
• While population characteristics (like heterogeneity) influence sampling strategy choices, Reason (R) does not directly explain *why* stratified sampling depends on SRS or *how* it increases representativeness. The reason addresses sample size needs based on population variability, not the mechanics or rationale behind stratified sampling itself.

Thus, both statements are correct, but (R) does not provide the correct explanation for (A).

Conclusion

Based on the analysis, both Assertion (A) and Reason (R) are factually correct statements. However, Reason (R) does not explain the mechanism or validity of Assertion (A). Therefore, the correct option is that both are correct, but (R) is not the correct explanation of (A).