You want to demonstrate that the mean of the sampling distribution is approximately equal to the population proportion. You have two sets of data to use: one is a sample size of 75, and the other is a sample size of 400. Which of the following statements is true?(1 point)

Question

Responses

The sample size of 75 will not give a better approximation of population proportion, as it has less variability in the data and is more symmetrical.
The sample size of 75 will not give a better approximation of population proportion, as it has less variability in the data and is more symmetrical.

The sample size of 400 will not give a better approximation of population proportion, as it has more variability and the mean falls close to the middle of the distribution.
The sample size of 400 will not give a better approximation of population proportion, as it has more variability and the mean falls close to the middle of the distribution.

The sample size of 400 will give a better approximation of population proportion, as it is symmetrical and the mean falls close to the middle of the distribution.
The sample size of 400 will give a better approximation of population proportion, as it is symmetrical and the mean falls close to the middle of the distribution.

The sample size of 75 will give a better approximation of population proportion, as it has more variability in the data and is less symmetric.

Answer 1

The correct response is:

The sample size of 400 will give a better approximation of population proportion, as it is symmetrical and the mean falls close to the middle of the distribution.

This statement is true as larger sample sizes tend to yield a sampling distribution that is closer to the true population proportion due to the law of large numbers. Larger samples reduce variability and result in a more accurate estimation of the population parameter, leading to a sampling distribution that is more symmetrical and concentrated around the true mean.