Ask a New Question
Menu

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

1 answer

The correct statement among the options provided is:

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

Explanation:

  1. Sample Size and Variability: A larger sample size, such as 400, tends to have less variability in the sample proportion, leading to a more accurate estimate of the population proportion compared to a smaller sample size, such as 75.

  2. Sampling Distribution: The sampling distribution of the sample proportion approaches a normal distribution as the sample size increases, according to the Central Limit Theorem. A sample size of 400 is more likely to yield a distribution that is symmetrical and centered around the true population proportion.

  3. Accuracy: Larger sample sizes generally provide better approximations of population parameters due to reduced sampling error.

In summary, with a larger sample size of 400, both the variability is reduced and the estimate is more likely to be symmetric, making it a better approximation of the population proportion than a smaller sample size of 75.