Which methods usually require smaller sample sizes than the Mean Per Unit (MPU) method?

The correct response indicates that both ratio and difference methods typically require smaller sample sizes compared to the Mean Per Unit (MPU) method. This is fundamentally due to the way these methods leverage existing information about the population.

Ratio estimation involves using a ratio of two variables to obtain a more precise estimate than what would be possible through simple averages. If previously established relationships exist between the sampled and total populations, this method can significantly refine the estimation process, leading to a higher efficiency that often translates into smaller required sample sizes.

Difference methods, on the other hand, focus on discrepancies between known values and estimated values to refine estimates. Similar to ratio methods, they exploit relationships within the data to provide more accurate estimates, which also results in a reduced requirement for sample sizes.

Conversely, the Mean Per Unit method relies solely on obtaining an average from the sampled units, which can lead to larger sampling errors and thus, necessitates larger sample sizes to achieve the same level of precision as ratio or difference methods. This is particularly important when the population is heterogeneous or when the element variances are high.

Collectively, these properties of ratio and difference methods underscore their ability to provide more reliable estimations with smaller sample sizes than the MPU method.