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:

Look at the inequality sign in the alternative hypothesis (\(H_1\)):
- If \(H_1: \theta > \theta_0\) \(\implies\) Right-tailed test.
- If \(H_1: \theta < \theta_0\) \(\implies\) Left-tailed test.
- If \(H_1: \theta \ne \theta_0\) \(\implies\) Two-tailed test.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A statistical hypothesis test can be one-tailed (directional) or two-tailed (non-directional).
The direction of the test is determined entirely by the alternative hypothesis (\(H_1\)).

Step 2: Detailed Explanation:
Let us analyze the structure of the hypothesis test given in the problem statement.
We have:
- Null Hypothesis (\(H_0\)): \(\phi_0 = 5\)
- Alternative Hypothesis (\(H_1\)): \(\phi_1 > 5\)
The alternative hypothesis states that the parameter of interest is strictly greater than the value specified under the null hypothesis.
Because we are only interested in detecting deviations in one specific direction (values significantly larger than 5), this is a one-tailed test.
Since the inequality sign in \(H_1\) points to the right (\(>\)), the critical region (or rejection region) lies entirely in the right tail of the sampling distribution of our test statistic.
If the test statistic falls in this extreme right region, we reject \(H_0\) in favor of \(H_1\).
Therefore, this test is classified as a right-tailed test.
For comparison:
- If \(H_1\) was \(\phi_1 < 5\), it would be a left-tailed test.
- If \(H_1\) was \(\phi_1 \ne 5\), it would be a two-tailed test.

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