Question

The difference between an estimate and the parameter is called :

• A. Sampling error
• B. Random error
• C. Probability error
• D. Non-sampling error

Hint:

\[ \text{Sampling Error} = \text{Estimate} - \text{Parameter} \]
As the sample size increases, the sampling error generally decreases, approaching zero when the sample size equals the population size.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In statistical inference, a parameter is a fixed, numerical characteristic of a population, while an estimate is a value calculated from a sample to approximate the parameter.

Step 2: Detailed Explanation:
The difference between the estimate (the value of the statistic calculated from a sample) and the true value of the population parameter is defined as the sampling error.
This error arises because a sample contains only a subset of the population, leading to natural statistical fluctuations.
Even if the sample is selected using an unbiased probability design, the estimate will rarely equal the true parameter exactly, and this discrepancy is called the sampling error.
Let us differentiate this from the other options:
- Non-sampling error: Errors that occur during data collection, recording, or processing, which can happen in both sample surveys and complete censuses.
- Random error: Fluctuations in measurements caused by unpredictable, uncontrollable variables.
- Probability error: A non-standard term occasionally used to describe errors linked to probability distributions, but not representing the parameter-estimate gap.

Step 3: Final Answer:
The difference between an estimate and the parameter is called Sampling error.