The correct answer is C) Haphazard sampling.

Haphazard sampling, also known as convenience sampling, is the least suitable method for extrapolating results to the population because it lacks the essential principles of randomness and systematic selection found in other sampling methods.

In haphazard sampling, the selection of elements in the sample is done in a non-random and non-systematic manner, often based on what is easiest or most convenient.

This approach can introduce significant bias and limit the generalizability of the results to the entire population. Let’s delve into the reasons why haphazard sampling is less suitable for extrapolating results and why the other options are more appropriate:

Why the correct answer is C) Haphazard sampling:

1. Lack of Randomness:

In haphazard sampling, there is no randomization involved in selecting sample elements. Randomization is a crucial principle in statistical sampling because it ensures that each element in the population has an equal chance of being included in the sample.

Without randomness, the sample is more likely to be unrepresentative of the population, as certain elements may be overrepresented, and others may be underrepresented or omitted altogether.

2. Selection Bias:

Haphazard sampling often leads to selection bias, as it allows the researcher to choose elements based on convenience or availability. This introduces subjectivity into the selection process, as the researcher may unintentionally or intentionally choose elements that support a particular perspective or hypothesis.

Selection bias can undermine the validity and reliability of the results and makes it difficult to generalize findings to the entire population.

3. Limited Control:

Haphazard sampling provides limited control over the sampling process. In systematic and random sampling methods, there are established procedures to ensure that every element in the population has an equal chance of being selected. In contrast, haphazard sampling lacks such controls, making it difficult to estimate the sampling error and draw valid statistical inferences.

4. Non-Representative Samples:

Haphazard sampling is prone to producing non-representative samples. A non-representative sample may not reflect the diversity and characteristics of the entire population, leading to unreliable extrapolations. The lack of randomness means that specific subgroups within the population may be underrepresented or overrepresented, which can distort the results.

Why the other options are not correct:

A) Systematic sampling:

Systematic sampling is a suitable method for extrapolating results to the population when the population exhibits a clear pattern or structure. It involves selecting every nth element from a list, which can provide a representative sample if the list is appropriately ordered.

Systematic sampling ensures that the sample is spread across the population in a systematic and even manner, increasing the likelihood of a representative sample.

B) Random sampling:

Random sampling is one of the most robust methods for generalizing results to the population. It involves selecting elements entirely at random, ensuring that every element in the population has an equal chance of being chosen.

Random sampling minimizes selection bias and provides a strong foundation for statistical inference. The principle of randomness is essential for obtaining unbiased estimates and valid generalizations.

D) None:

This option suggests that no sampling method is least suitable for extrapolating results to the population. However, as discussed earlier, haphazard (convenience) sampling lacks the crucial principles of randomness and systematicity, making it less suitable for generalizing findings to the entire population.

The other options, systematic and random sampling, are more suitable because they adhere to these principles.

In summary, haphazard sampling (convenience sampling) is the least suitable method for extrapolating results to the population due to its lack of randomness, potential for selection bias, limited control, and the likelihood of producing non-representative samples.

In contrast, systematic and random sampling methods adhere to principles that enhance the representativeness and reliability of the sample, making them more appropriate for statistical inference and generalization to the population.