Question
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)
Responses
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.
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.
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 not give a better approximation of population proportion, as it has less variability in the data and is more symmetrical.
Responses
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.
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.
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 not give a better approximation of population proportion, as it has less variability in the data and is more symmetrical.
Answers
GPT-4o mini
The correct statement 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.**
Here's the reasoning:
1. Larger sample sizes tend to provide better estimates of population parameters due to the Central Limit Theorem, which states that as sample size increases, the sampling distribution of the sample mean (or proportion) approaches a normal distribution regardless of the shape of the population distribution.
2. A sample size of 400 is larger than a sample size of 75, and thus it typically exhibits less variability and a more symmetric distribution around the population proportion, making the estimate of the population proportion more accurate.
3. Smaller samples (like 75) can have higher variability and may not be as symmetric, which can lead to less reliable estimates of the population proportion.
Thus, the sample size of 400 is better for approximating the population proportion.
**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.**
Here's the reasoning:
1. Larger sample sizes tend to provide better estimates of population parameters due to the Central Limit Theorem, which states that as sample size increases, the sampling distribution of the sample mean (or proportion) approaches a normal distribution regardless of the shape of the population distribution.
2. A sample size of 400 is larger than a sample size of 75, and thus it typically exhibits less variability and a more symmetric distribution around the population proportion, making the estimate of the population proportion more accurate.
3. Smaller samples (like 75) can have higher variability and may not be as symmetric, which can lead to less reliable estimates of the population proportion.
Thus, the sample size of 400 is better for approximating the population proportion.