Question

Increasing the sample size has the following effect upon the sampling error :

• A. It increases the sampling error
• B. It increases the standard error of the estimate
• C. It decreases the sampling error
• D. It has no effect

Hint:

A larger sample size always leads to more precise estimates. Therefore, as $n \to N$, the sampling error approaches $0$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Sampling error represents the discrepancy between a sample statistic (like the sample mean $\bar{y}$) and the true population parameter (like the population mean $\mu$).
It is measured by the Standard Error ($SE$).
Key Formula or Approach:
The standard error of the sample mean is given by: \[ SE = \frac{\sigma}{\sqrt{n}} \] Where: - $\sigma$ is the population standard deviation.
- $n$ is the sample size.

Step 2: Detailed Explanation:
From the formula, we see that the Standard Error is inversely proportional to the square root of the sample size: \[ SE \propto \frac{1}{\sqrt{n}} \] - As the sample size ($n$) increases, the denominator ($\sqrt{n}$) increases.
- This causes the overall Standard Error ($SE$) to decrease.
- Consequently, a larger sample size provides a more representative subset of the population, reducing the sampling error.

Step 3: Final Answer:
Increasing the sample size decreases the sampling error, matching Option (C).