Question

According to the Central Limit Theorem, which statements(s) are TRUE. There may be more than 1 correct answer. A. An increase in sample size from n = 16 to n = 25 will produce a sampling distribution for the sample means that has a smaller standard deviation. B. The larger the sample size, the more the sampling distribution of sample means will resemble a normal distribution C. The mean of the sampling distribution of sample means for samples of size n = 15 will be the same as the mean of the sampling distribution for samples of size n = 100. D. The mean of a sampling distribution of sample means is equal to the population mean divided by the square root of the sample size. E. The larger the sample size, the more the sampling distribution of sample means resembles the shape of the population.

Answer 1

Answer:

Options A, B and C are correct.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

From the Central Limit Theorem, we have that:

The larger the sample size, the closer to the normal distribution the distribution of sample means is.

No matter the sample size, the mean is the same.

The larger the sample size, the smaller the standard deviation.

The smaller the sample size, the larger the standard deviation.

So the correct options are:

A, B, C