Correct option is B
The correct answer is (b).
Introduction
In research methodology and statistics, determining the correct sample size is pivotal for drawing valid conclusions about a population.
The sample size must be carefully calibrated to balance cost, time, and the desired level of accuracy.
Key factors influencing this include the required precision of the estimate and the underlying variance within the population.
Information Booster
- Precision refers to how close the sample estimates are to the true population parameters.
- Higher precision requirements directly mandate careful calculation of sample size (Statement 1 is correct).
- Statistically, the standard error of a sample statistic decreases as the sample size increases.
- Thus, for greater precision and smaller error margins, a larger sample is scientifically required (Statement 2 is correct, contradicting Statement 3).
- Heterogeneity refers to the amount of variation or diversity within the population.
- If a population is highly varied, a larger sample is needed to adequately capture all subgroups and characteristics accurately (Statement 4 is correct).
- Conversely, if a population is highly homogeneous (uniform), a smaller sample can easily represent the whole.
- Therefore, the correct synthesis of sampling theory validates statements 1, 2, and 4.
- Option A (1, 2 and 3): Incorrect because statement 3 is fundamentally flawed. A smaller sample size increases the margin of error and decreases statistical precision.
- Option C (1, 3 and 4): Incorrect due to the inclusion of statement 3, which contradicts established statistical sampling theory regarding sample size and precision.
- Option D (2, 3 and 4): Incorrect because statements 2 and 3 are diametrically opposite; they cannot both be true simultaneously. Moreover, it leaves out the foundational truth of statement 1.
English
10 Questions
20 Marks
12 Mins
