Question

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

Answer 1

The statement that is false as \( n \) (the sample size) in a sampling distribution increases is:

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

In a sampling distribution, as the sample size increases, the variability (measured by the standard error) typically decreases, and the distribution of sample means (or proportions) tends to center around the population mean (or proportion). Additionally, the distribution becomes more symmetric and approaches a normal distribution due to the Central Limit Theorem. However, the range of the data does not necessarily increase with larger sample sizes; it can actually stabilize. Therefore, this statement is incorrect.