Question

In testing of hypothesis, whether a critical region is one sided or two sided depends on

• A. Null hypothesis
• B. Alternate Hypothesis
• C. Simple Hypothesis
• D. Composite Hypothesis

Hint:

The null hypothesis sets the baseline, while the alternate hypothesis sets the direction of the test. Look at $H_1$ to decide whether to perform a one-tailed or two-tailed test.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The critical region (rejection region) contains the set of all outcomes of a test statistic that lead to the rejection of the null hypothesis.

Step 2: Detailed Explanation:
The null hypothesis $H_0$ usually specifies a state of no difference or no effect (e.g., $H_0: \mu = \mu_0$).
The alternative (alternate) hypothesis $H_1$ defines the direction of the deviation we are looking for:
- Two-sided test: The alternative hypothesis is non-directional ($H_1: \mu \neq \mu_0$). The rejection region is split between both the lower and upper tails of the distribution.
- One-sided test: The alternative hypothesis is directional ($H_1: \mu > \mu_0$ or $H_1: \mu < \mu_0$). The rejection region lies entirely in a single tail of the distribution.
Therefore, whether a critical region is one-sided or two-sided is determined entirely by the Alternate Hypothesis.

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