Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
As the size of a sample increases, the mean of the distribution of sample means increases.
Choose the correct answer below.
A. False. As the size of a sample increases, the mean of the distribution of sample means decreases.
B. False. As the size of a sample increases, the mean of the distribution of sample means does not change.
C. True.

Step 1 ：The statement is referring to the concept of the Central Limit Theorem in statistics. According to the Central Limit Theorem, as the size of a sample increases, the distribution of sample means approaches a normal distribution. However, the mean of the distribution of sample means does not change with the increase in sample size. It remains the same as the population mean.

Step 2 ：Therefore, the statement is false. The correct statement should be 'As the size of a sample increases, the mean of the distribution of sample means does not change.'

Step 3 ：\(\boxed{\text{B. False. As the size of a sample increases, the mean of the distribution of sample means does not change.}}\)