The question asks about the behavior of the mean and variability of a sampling distribution as the sample size decreases.

Answer Explanation:

1. Mean of the Sampling Distribution:

   • The mean of the sampling distribution (often called the expected value) remains the same as the sample size changes. It is equal to the population mean, regardless of the sample size.

2. Variability of the Sampling Distribution:

   • The variability (standard error) of the sampling distribution increases as the sample size decreases. The standard error is inversely related to the square root of the sample size ($\text{SE} = \frac{\sigma}{\sqrt{n}}$). As $n$ decreases, $\text{SE}$ increases, making the distribution more spread out.

Correct Answer:

A. The mean of the sampling distribution remains the same, and the variability increases.

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Related Questions:

1. How does increasing the sample size affect the standard error of the mean?
2. What is the relationship between sample size and the accuracy of sample estimates?
3. Why does the mean of the sampling distribution remain unchanged with sample size changes?
4. How does the Central Limit Theorem influence the shape of the sampling distribution?
5. What happens to the confidence interval width as sample size decreases?

Tip:

Remember, as sample size decreases, the precision of your estimates decreases, which is reflected by an increase in variability.