Question
The figure shows how the distribution of a sampling proportion appears when the sample size is n=10 , n=100 , and n=1,000 . How does the range change as n becomes larger?
(1 point)
Responses
The range becomes smaller.
The range becomes smaller.
The range cannot be determined from the graph.
The range cannot be determined from the graph.
The range remains constant.
The range remains constant.
The range becomes larger.
(1 point)
Responses
The range becomes smaller.
The range becomes smaller.
The range cannot be determined from the graph.
The range cannot be determined from the graph.
The range remains constant.
The range remains constant.
The range becomes larger.
Answers
GPT-4o mini
As the sample size \( n \) becomes larger, the range of the sampling proportion becomes smaller. This is due to the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample proportion approaches a normal distribution with a smaller standard error, resulting in less variability among the sample proportions.
Therefore, the correct response is:
**The range becomes smaller.**
Therefore, the correct response is:
**The range becomes smaller.**