Question

The distribution that is formed by all possible values of a statistics is known as:

• A. Normal distribution
• B. Binomial distribution
• C. Sampling distribution
• D. Uniform distribution

Hint:

Remember the definition:
- Distribution of a Population $\rightarrow$ Population Distribution
- Distribution of a Sample $\rightarrow$ Sample Distribution
- Distribution of a Statistic (across all possible samples) $\rightarrow$ Sampling Distribution

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In statistical inference, we draw samples from a population to estimate population parameters.
A "statistic" is a numerical characteristic calculated from a sample (e.g., sample mean, sample proportion, or sample standard deviation).

Step 2: Detailed Explanation:
If we draw all possible independent random samples of a fixed size $n$ from a population, the value of a given statistic will vary from sample to sample.
- Sampling Distribution: The probability distribution of these sample values of the statistic is called its sampling distribution.
For example, the sampling distribution of the mean describes how the sample mean behaves across different samples.
- The standard deviation of this sampling distribution is called the standard error of the statistic.
- In contrast, the Normal, Binomial, and Uniform distributions are general probability distributions that can model either populations, samples, or theoretical processes, but they are not defined as the distribution of a statistic across all possible samples.
Therefore, the correct term is the sampling distribution.

Step 3: Final Answer:
The distribution formed by all possible values of a statistic is known as the Sampling distribution.