Question

What is the correct decision in a hypothesis if the data produce a t-statistic that is in the critical region

• A. Reject H0
• B. Fail to reject H0
• C. Reject H1
• D. Fail to reject H1

Hint:

Critical Region = Rejection Region.
If the calculated statistic falls in the critical region, reject \( H_0 \) (and accept \( H_1 \)).
This corresponds to a p-value less than the chosen significance level (\( \alpha \)).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In statistical hypothesis testing, we formulate a null hypothesis (\( H_0 \)) and an alternative hypothesis (\( H_1 \)).
A test statistic (such as the t-statistic) is calculated from the sample data to determine whether there is sufficient evidence to support or reject \( H_0 \).

Step 2: Detailed Explanation:
The distribution of the test statistic is divided into two regions based on a chosen significance level (\( \alpha \)):
1. The acceptance region (non-critical region): The range of values where any variation is considered to be due to random sampling, meaning we fail to reject \( H_0 \).
2. The critical region (rejection region): The range of values that are highly unlikely to occur if the null hypothesis is true.
If the calculated t-statistic falls within the critical region, it indicates that the observed sample difference is statistically significant and highly unlikely to be due to chance.
Therefore, the standard statistical decision under these conditions is to reject the null hypothesis (\( H_0 \)) and accept the alternative hypothesis (\( H_1 \)).

Step 3: Final Answer:
If the t-statistic is in the critical region, the correct decision is to reject H0.