Suppose the observed value of the test equals 2.45 and the critical value of the rejection region for a right tailed test equals 2.281. What is the decision of the test? Suppose the observed value of the test equals -1.95 and the critical value of the rejection region for a left tailed test equals -2.371. What is the decision of the test?

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### Hypothesis Testing Critical Values and Decision Making

#### Example 1: Right-Tailed Test
**Scenario:**  
Suppose the observed value of the test equals 2.45 and the critical value of the rejection region for a right-tailed test equals 2.281. What is the decision of the test?

**Solution:**  
In this scenario, the observed value (2.45) is greater than the critical value (2.281). For a right-tailed test, if the observed value of the test statistic exceeds the critical value, we reject the null hypothesis.

**Decision:**  
Reject the null hypothesis.

#### Example 2: Left-Tailed Test
**Scenario:**  
Suppose the observed value of the test equals -1.95 and the critical value of the rejection region for a left-tailed test equals -2.371. What is the decision of the test?

**Solution:**  
In this scenario, the observed value (-1.95) is greater than the critical value (-2.371). For a left-tailed test, if the observed value of the test statistic is greater than the critical value, we fail to reject the null hypothesis.

**Decision:**  
Fail to reject the null hypothesis.
Transcribed Image Text:### Hypothesis Testing Critical Values and Decision Making #### Example 1: Right-Tailed Test **Scenario:** Suppose the observed value of the test equals 2.45 and the critical value of the rejection region for a right-tailed test equals 2.281. What is the decision of the test? **Solution:** In this scenario, the observed value (2.45) is greater than the critical value (2.281). For a right-tailed test, if the observed value of the test statistic exceeds the critical value, we reject the null hypothesis. **Decision:** Reject the null hypothesis. #### Example 2: Left-Tailed Test **Scenario:** Suppose the observed value of the test equals -1.95 and the critical value of the rejection region for a left-tailed test equals -2.371. What is the decision of the test? **Solution:** In this scenario, the observed value (-1.95) is greater than the critical value (-2.371). For a left-tailed test, if the observed value of the test statistic is greater than the critical value, we fail to reject the null hypothesis. **Decision:** Fail to reject the null hypothesis.
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