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 of variability and the shape of the distribution change as the sample size becomes larger?
Option #1: As sample size increases, the range or variability decreases, and the shape of the distribution becomes more symmetric.
Option #2 As sample size increases, the range or variability increases, and the shape of the distribution becomes more symmetric.
(1 point)
Option
Option #1: As sample size increases, the range or variability decreases, and the shape of the distribution becomes more symmetric.
Option #2 As sample size increases, the range or variability increases, and the shape of the distribution becomes more symmetric.
(1 point)
Option
Answers
GPT-4o mini
The correct option is **Option #1**: As sample size increases, the range of variability decreases, and the shape of the distribution becomes more symmetric.
As the sample size increases, the variability of the sampling distribution of the proportion decreases due to the Law of Large Numbers. Additionally, according to the Central Limit Theorem, the sampling distribution approaches a normal distribution (which is symmetric) as sample size increases, regardless of the shape of the population distribution.
As the sample size increases, the variability of the sampling distribution of the proportion decreases due to the Law of Large Numbers. Additionally, according to the Central Limit Theorem, the sampling distribution approaches a normal distribution (which is symmetric) as sample size increases, regardless of the shape of the population distribution.