Question

Question

Which of the following statements do you recognize as being false as n, in a sampling distribution, increases?(1 point)
Responses

The range of the data becomes larger as n increases.
The range of the data becomes larger as n increases.

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.

Answer 1

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

The range of the data becomes larger as n increases.

In general, as the sample size \( n \) increases, the range of the sample may vary, but the general expectation is that larger samples tend to provide estimates of the population parameters that are more stable, and the variability of sample statistics (like the mean) decreases.

The other statements regarding the variability of data, centering around the population proportion, and the shape becoming more symmetric are true in the context of the Central Limit Theorem and the law of large numbers.