The correct answer is: (a) and (c) both.
Area sampling is a type of sampling that divides the population into geographic areas, such as neighborhoods or counties, and then selects a sample of those areas. The individuals within each selected area are then surveyed.
Area sampling is often used when the population is large and scattered. It can be more efficient than other types of sampling, such as simple random sampling, because it requires fewer interviews.
Area sampling can also be used when the population is heterogeneous. Heterogeneity refers to the degree to which the individuals in a population differ from one another. If the population is heterogeneous, it may be difficult to obtain a representative sample using simple random sampling. Area sampling can help to ensure that the sample is representative of the population by selecting areas that are similar to the population as a whole.
However, area sampling can be more difficult to implement than other types of sampling. It requires careful planning and execution. Additionally, it can be more expensive than other types of sampling.
Here are some additional details about each option:
- Option A: Population is scattered and large size from which the sample is to be drawn. This is a common situation in which area sampling is used. For example, if you want to survey a population of people living in a large city, it would be difficult to select a simple random sample of individuals. However, you could divide the city into geographic areas, such as neighborhoods, and then select a sample of those areas. This would be more efficient than trying to select a simple random sample of individuals.
- Option B: The population is heterogeneous. This is another common situation in which area sampling is used. For example, if you want to survey a population of people living in a large city, the population will likely be heterogeneous in terms of age, race, ethnicity, income, and other characteristics. If you try to select a simple random sample of individuals, you may not get a representative sample of the population. However, if you divide the city into geographic areas and then select a sample of those areas, you will be more likely to get a representative sample of the population.
- Option C: A long survey is needed. Area sampling can be used when a long survey is needed. This is because area sampling can be more efficient than other types of sampling, such as simple random sampling. Additionally, area sampling can help to ensure that the sample is representative of the population by selecting areas that are similar to the population as a whole.
Overall, area sampling is a useful tool for collecting data from large and heterogeneous populations. It can be more efficient than other types of sampling, and it can help to ensure that the sample is representative of the population. However, area sampling can be more difficult to implement than other types of sampling.