The statement in the image is:

"As the size of a sample increases, the mean of the distribution of sample means increases."

This statement is false. The mean of the distribution of sample means, also known as the expected value of the sample mean, does not change as the sample size increases. The mean of the distribution of sample means remains equal to the population mean, regardless of the sample size.

So, the correct answer is:

C. False. As the size of a sample increases, the mean of the distribution of sample means does not change.

Would you like further explanation or have any questions about this? Here are a few related questions to explore further:

1. How does sample size affect the variability of sample means?
2. What is the relationship between sample size and the standard error of the mean?
3. How does the Central Limit Theorem relate to sample means?
4. What is the formula for calculating the standard deviation of the sampling distribution?
5. Why does the mean of the sample means stay the same regardless of sample size?

Tip: The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution, regardless of the shape of the population distribution.