Question

Sampling Variability in the Sample Proportion Quick Check
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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.

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

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.
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Answer 1

"The range of the data becomes larger as n increases." is false.

Explanation: As sample size n increases, the sampling distribution of the sample proportion gets less variable (smaller standard error) and concentrates more tightly around the population proportion; its empirical range therefore tends to shrink, not grow. The shape also becomes more symmetric (approaching normal) provided np and n(1−p) are large enough.