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 standard deviation of the distribution of sample means increases.
Choose the correct choice below.
A. This statement is true.
B. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases."
C. This statement is false. A true statement is, "As the size of a sample decreases, the standard deviation of the distribution of sample means decreases."
D. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means does not change."
Answer
Final Answer: \(\boxed{\text{The correct choice is B. 'This statement is false. A true statement is, 'As the size of a sample increases, the standard deviation of the distribution of sample means decreases.'}}\)
Step 1 ：Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
Step 2 ：As the size of a sample increases, the standard deviation of the distribution of sample means increases.
Step 3 ：Choose the correct choice below.
Step 4 ：A. This statement is true.
Step 5 ：B. This statement is false. A true statement is, 'As the size of a sample increases, the standard deviation of the distribution of sample means decreases.'
Step 6 ：C. This statement is false. A true statement is, 'As the size of a sample decreases, the standard deviation of the distribution of sample means decreases.'
Step 7 ：D. This statement is false. A true statement is, 'As the size of a sample increases, the standard deviation of the distribution of sample means does not change.'
Step 8 ：The statement is false. According to the Central Limit Theorem, as the size of a sample increases, the standard deviation of the distribution of sample means decreases. This is because as we take more samples, we get a better estimate of the population mean, and thus our sample means are less spread out (i.e., have a smaller standard deviation).
Step 9 ：Final Answer: \(\boxed{\text{The correct choice is B. 'This statement is false. A true statement is, 'As the size of a sample increases, the standard deviation of the distribution of sample means decreases.'}}\)
