**Which of the following features is most important for random-based selection?**

** ****Options:**

a) Sample should be drawn form population b) Every strata of population should be represented in the sample c) Every item in the population has an equal chance of being selected in the sample d) Items should be selected at ‘n’ th interval |

### The Correct Answer Is:

c) Every item in the population has an equal chance of being selected in the sample

**Correct Answer Explanation:**

**c) Every item in the population has an equal chance of being selected in the sample.**

This statement defines the essence of randomness in sampling. In a truly random selection, each item in the population must have an equal probability of being chosen for the sample. This principle ensures that bias is minimized, allowing for a representative sample that mirrors the population characteristics.

When every item has an equal chance of selection, it prevents any particular subgroup or characteristic from being overrepresented or underrepresented in the sample, thus maintaining the fairness and accuracy of the sampling process.

**Explanation of Other Options:**

**a) Sample should be drawn from the population:**

This statement emphasizes the necessity of drawing the sample from the entire population under study, ensuring that the sample is representative. However, the act of drawing a sample from the population does not inherently guarantee randomness.

Even if the sample is taken from the entire population, the selection process might still introduce biases if it’s not conducted randomly.

For instance, if the sampling method involves non-random selection or if certain parts of the population have a higher chance of being included in the sample, the resulting sample might not accurately reflect the population’s diversity and characteristics.

**b) Every strata of the population should be represented in the sample:**

Stratified sampling aims to ensure that different subgroups or strata within the population are represented in the sample. This technique involves dividing the population into distinct groups based on certain characteristics and then independently sampling from each subgroup.

While this method is beneficial for ensuring proportional representation of various segments of the population, it doesn’t guarantee random selection within each stratum. Without ensuring that every item within each stratum has an equal chance of being selected, biases might arise, especially if the selection within each subgroup isn’t random.

**d) Items should be selected at ‘n’th interval:**

Systematic sampling involves selecting items at regular intervals from an ordered list. For instance, every 5th person on a list might be chosen for the sample. While this method might seem systematic and organized, it can introduce bias if there’s any underlying periodicity or pattern in the population.

If the list is arranged in such a way that certain characteristics repeat at regular intervals, selecting items at fixed intervals could inadvertently skew the sample, missing variations or unique attributes within the population that are not aligned with the interval pattern.

The critical aspect in random-based selection is ensuring that every individual item within the population has an equal chance of being selected for the sample.

This equal probability principle, which is inherent in true random sampling, ensures that the sample is unbiased and accurately represents the diversity and characteristics of the entire population, making option (c) the most crucial factor in random-based selection.

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