Which of the following sampling procedures would be an example of random sampling?
1 Selecting a unit of production from the middle of the hourly production mixture.
2 Selecting a unit of product based on serial numbers of the product and a random number table.
3 Sorting the production units into groups based on color and then selecting a unit based on the most commonly produced color.
4 Selecting the unit of product from a continuous production stream at 10 minutes after the hour.
The correct answer and explanation is :
The correct answer is 2. Selecting a unit of product based on serial numbers of the product and a random number table.
Explanation:
In statistical sampling, random sampling refers to a method where every individual unit in a population has an equal chance of being selected for the sample. This ensures that the sample is representative of the entire population, which is crucial for making valid generalizations.
Now, let’s break down each option:
- Selecting a unit of production from the middle of the hourly production mixture:
This is not random sampling. The selection is based on a specific time or place (the “middle” of the production mixture), which introduces bias. The unit selected may not represent the full range of units produced throughout the hour, as the middle point may differ significantly from units produced at the start or end of the hour. - Selecting a unit of product based on serial numbers of the product and a random number table:
This is a random sampling technique. The serial numbers represent a complete list of all units produced, and using a random number table ensures that each serial number has an equal chance of being selected. This method is unbiased, as it doesn’t favor any particular unit or set of units, and is a classic example of random sampling. - Sorting the production units into groups based on color and then selecting a unit based on the most commonly produced color:
This is not random sampling. The method introduces bias by selecting units based on color, which limits the diversity of the sample. Random sampling requires that every unit has an equal chance of being selected, not just those from the most common group. - Selecting the unit of product from a continuous production stream at 10 minutes after the hour:
This is also not random sampling. By choosing a unit at a fixed time (10 minutes after the hour), the sample may be skewed, as certain patterns or variations in production could be tied to specific times.
In conclusion, the second option, where units are selected randomly using a number table, is the only method that ensures every product has an equal chance of being chosen, which is the key feature of random sampling.