Question

Testing $H_0: \mu = 0$ vs $H_1: \mu > 0$ is a

• A. left tailed test
• B. right tailed test
• C. two tailed test
• D. vertical test

Hint:

The inequality sign in $H_1$ acts like an arrow pointing to the direction of the tail:
- $\mu > \mu_0$ points right ($\rightarrow$ right-tailed).
- $\mu < \mu_0$ points left ($\leftarrow$ left-tailed).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The direction of the alternative hypothesis $H_1$ determines the location of the critical region (rejection region) on the test statistic's distribution curve.

Step 2: Detailed Explanation:
Let us classify tests based on the alternative hypothesis $H_1$:
- Two-tailed test: The alternative hypothesis uses a "not equal to" sign ($H_1: \mu \neq \mu_0$). The critical region is split equally between both tails of the distribution.
- One-tailed test: The alternative hypothesis uses an inequality sign ($>$ or $<$):
1. Left-tailed test: Uses the "less than" sign ($H_1: \mu < \mu_0$). The critical region lies entirely in the left tail of the distribution.
2. Right-tailed test: Uses the "greater than" sign ($H_1: \mu > \mu_0$). The critical region lies entirely in the right tail of the distribution.
Since the alternative hypothesis in this question is $H_1: \mu > 0$, it is a right-tailed test.

Step 3: Final Answer
The correct option is (B).