Question

which of the following statements do you recognize as being false as n, in a sampling distribution, increases? (1 point)
the distribution or shape of the data becomes more symmetric as n increases.
the variability of the data becomes smaller as n gets larger.
the range of the data becomes larger as n increases.
as n increases, the data centers more around the population proportion.

Explanation:

• For the first statement: By the Central Limit Theorem, as sample size \( n \) increases, the sampling distribution becomes more symmetric (approaches normal), so this is true.
• For the second statement: Variability (e.g., standard error) is related to \( \frac{\sigma}{\sqrt{n}} \), so as \( n \) increases, variability decreases, making this true.
• For the third statement: The range of a sampling distribution (or data) does not necessarily become larger as \( n \) increases. In fact, with larger \( n \), the data clusters more around the population parameter, so range is not expected to increase. This is false.
• For the fourth statement: As \( n \) increases, the sampling distribution centers more around the population proportion (by properties of sampling distributions), so this is true.

Answer:

The range of the data becomes larger as \( n \) increases.