Mark ‘TRUE’ or ‘FALSE’ for each of the following.
$\left(C\right)$ You should always reject $H_0$ if the test statistic is greater than the critical value.

• A. TRUE
• B. FALSE
• C. Cannot be determined

Answer: (B)

Verified step by step guidance

1. Understand the hypothesis testing framework: The null hypothesis \(H_0\) is tested against an alternative hypothesis \(H_a\) using a test statistic calculated from sample data.
2. Identify the type of test and the direction of the rejection region: For a right-tailed test, you reject \(H_0\) if the test statistic is greater than the critical value; for a left-tailed test, you reject \(H_0\) if the test statistic is less than the critical value; for a two-tailed test, you reject \(H_0\) if the test statistic is either greater than the upper critical value or less than the lower critical value.
3. Recognize that the statement 'You should always reject \(H_0\) if the test statistic is greater than the critical value' is not universally true because it depends on the type of test and the critical value's position.
4. Therefore, the correct approach is to compare the test statistic to the critical value(s) according to the specific test's rejection region(s), not to apply a blanket rule for all tests.
5. Conclude that the statement is FALSE because it ignores the context of the test direction and the nature of the critical value(s).