As \( n \), the sample size in a sampling distribution, increases, the following statements can be evaluated:
A. The variability of the data becomes smaller as \( n \) gets larger.
- This statement is true. As the sample size increases, the standard error of the mean (or proportion) decreases, leading to smaller variability in the sampling distribution.
B. The range of the data becomes larger as \( n \) increases.
- This statement is false. The range of a sample does not necessarily get larger as sample size increases. In fact, a larger sample may provide a more accurate estimate of the population parameters, but it does not imply that the range itself will increase.
C. The distribution or shape of the data becomes more symmetric as \( n \) increases.
- This statement is true. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample means (or proportions) approaches a normal distribution, regardless of the shape of the population distribution, making it more symmetric.
D. As \( n \) increases, the data centers more around the population proportion.
- This statement is true. Larger sample sizes result in sample estimates (such as sample means or proportions) being closer to the true population parameters, leading to increased accuracy.
Therefore, the false statement among the given options is B: The range of the data becomes larger as \( n \) increases.