Which of the following is not true for a hypothesis test for correlation?

• A. The test statistic is often based on the sample correlation coefficient $r$.
• B. The test can be used to determine if one variable causes changes in the other variable.
• C. The null hypothesis typically states that the population correlation coefficient $\rho$ is equal to zero.
• D. A significant result indicates that there is a linear relationship between the two variables in the population.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the purpose of a hypothesis test for correlation. It is used to determine whether there is evidence of a linear relationship between two variables in the population, based on the sample data.
2. Step 2: Recall that the test statistic for correlation is typically based on the sample correlation coefficient \(r\), which measures the strength and direction of the linear relationship between two variables.
3. Step 3: Know the null hypothesis (\(H_0\)) in this test usually states that the population correlation coefficient \(\rho\) is zero, meaning no linear relationship exists between the variables.
4. Step 4: Recognize that a significant test result suggests there is a linear relationship between the two variables in the population, but it does not imply causation.
5. Step 5: Therefore, the statement that the test can be used to determine if one variable causes changes in the other variable is not true, because correlation does not imply causation.