To solve the given matching problem between List-I and List-II, we need to understand the definitions and characteristics of the terms involved:
- Randomization is used in: This is related to probability sampling, where randomization ensures that every member of the population has a known, non-zero chance of being selected, making the process unbiased. Thus it matches with II. Probability sampling.
- Randomization is not used in: This refers to non-probability sampling, where the selection of samples is not by random chance, potentially leading to bias. This matches with IV. Non-probability sampling.
- If every element in the population has an equal chance to be part of the selected sample, then the sampling process is called: This describes unbiased sampling where randomization ensures equality of selection. Hence, it matches with I. Unbiased sampling.
- If a sampling process systematically favours certain outcomes over others, then it is called: This defines a biased approach, which intentionally or unintentionally gives preference to certain outcomes. Therefore, it is linked with III. Biased sampling.
After making these connections, the correct matches are:
- A-II: Randomization is used in Probability sampling.
- B-IV: Randomization is not used in Non-probability sampling.
- C-I: If every element in the population has an equal chance, it is Unbiased sampling.
- D-III: If a sampling process systematically favours certain outcomes, it is Biased sampling.
Thus, the correct answer is: A-II, B-IV, C-I, D-III.