To determine the correct decision for the hypothesis test, follow these detailed steps:
1. Identify the given values:
- Test value (also known as the test statistic): 2.57
- Critical value: 1.96
2. Understand the hypothesis test set-up:
- Null Hypothesis (H₀): This usually represents the statement that there is no effect or no difference. For example, it may state that the means of two samples are equal.
- Alternative Hypothesis (H₁): This usually represents the statement that there is an effect or a difference. For instance, it may state that the means of two samples are not equal.
3. Determine the decision rule:
- A common rule in hypothesis testing is to compare the test value to the critical value.
- If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis (H₀).
- If the absolute value of the test statistic is less than or equal to the critical value, we do not reject the null hypothesis (H₀).
4. Compare the test value to the critical value:
- The test value is 2.57.
- The critical value is 1.96.
- Check if 2.57 is greater than 1.96.
5. Make the decision:
- Since 2.57 is greater than 1.96, we reject the null hypothesis (H₀).
6. Select the correct answer based on the decision:
- Rejecting the null hypothesis corresponds to option A.
So the decision should be:
A) Reject the null hypothesis.
