Question

Consider a hypothesis \(H_0\) where \(\phi_0 = 5\) against \(H_1\) where \(\phi_1 > 5\). The test is :

• A. Right tailed
• B. Left tailed
• C. Center tailed
• D. Cross tailed

Hint:

Always look at the inequality sign in the alternative hypothesis \(H_1\):
- \(>\) points to the right \(\implies\) Right-tailed test.
- \(<\) points to the left \(\implies\) Left-tailed test.
- \(\neq\) means both directions \(\implies\) Two-tailed test.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The direction of a statistical test is determined entirely by the alternative hypothesis \(H_1\).
Based on the inequality or equality sign in the alternative hypothesis, a test can be one-tailed (either right-tailed or left-tailed) or two-tailed.

Step 2: Detailed Explanation:
Let us analyze the hypotheses given in the problem statement.
The null hypothesis is formulated as:
\[ H_0: \phi = \phi_0 = 5 \]
The alternative hypothesis is formulated as:
\[ H_1: \phi = \phi_1 > 5 \]
Since the alternative hypothesis specifies that the parameter of interest is strictly greater than the value under the null hypothesis (\(\phi > 5\)), we are only interested in deviations in the positive direction.
This means that extremely large values of the test statistic will provide evidence against the null hypothesis in favor of the alternative hypothesis.
Consequently, the critical region (or rejection region) lies entirely in the right tail of the probability distribution of the test statistic.
Therefore, the test is a right-tailed (or right-sided) test.
If the alternative hypothesis had been \(\phi < 5\), the test would be left-tailed.
If the alternative hypothesis had been \(\phi \neq 5\), the test would be two-tailed.

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