Do students perform the same when they take an exam alone as when they take an exam in a classroom setting? Eight students were given two tests of equal difficulty. They took one test in a solitary room and they took the other in a room filled with other students. The results are shown below. Exam Scores Alone 75 81 78 80 74 84 84 89 Classroom 82 83 84 77 84 91 93 99 Assume a Normal distribution. What can be concluded at the the a = 0.10 level of significance level of Hanificanco

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**Title: Analyzing Exam Performance in Different Settings**

**Introduction to the Study:**

The study aims to determine if students perform differently on exams taken in solitude versus in a classroom setting. Eight students were administered two tests of similar difficulty: one taken alone and the other in a classroom with peers. Their scores are as follows:

**Exam Scores Table:**

- **Alone**: 75, 81, 78, 80, 74, 84, 84, 89
- **Classroom**: 82, 83, 84, 77, 84, 91, 93, 99

**Hypothesis Testing Framework:**

- **Assumption**: Normal distribution.
- **Significance Level**: α = 0.10

**Steps in Statistical Analysis:**

1. **Hypotheses Formulation:**
   - **Null Hypothesis (H₀):** Population mean test score is the same in both settings.
   - **Alternative Hypothesis (H₁):** Population mean test score differs between settings.

2. **Test Selection:**
   - A suitable statistical test needs to be chosen for this comparative analysis.

3. **Calculation Requirements:**
   - **Test Statistic**: To be calculated (enter answer to 3 decimal places).
   - **P-value**: To be calculated (enter answer to 4 decimal places).

4. **Decision Criteria:**
   - Compare p-value with α (0.10) to determine statistical significance.

5. **Conclusion Determination:**
   - Decide to accept or reject the null hypothesis based on test results.

6. **Final Conclusion Options:**
   - **Option 1**: Results are statistically significant, suggesting a difference in performance settings.
   - **Option 2**: Results are not statistically significant, suggesting no difference.
   - **Option 3**: Results indicate no difference in average scores for the students.
   - **Option 4**: Results not statistically significant, suggesting equality in performance.

This study aims to provide insights on whether exam environments impact student performance and guide instructional strategies accordingly.
Transcribed Image Text:**Title: Analyzing Exam Performance in Different Settings** **Introduction to the Study:** The study aims to determine if students perform differently on exams taken in solitude versus in a classroom setting. Eight students were administered two tests of similar difficulty: one taken alone and the other in a classroom with peers. Their scores are as follows: **Exam Scores Table:** - **Alone**: 75, 81, 78, 80, 74, 84, 84, 89 - **Classroom**: 82, 83, 84, 77, 84, 91, 93, 99 **Hypothesis Testing Framework:** - **Assumption**: Normal distribution. - **Significance Level**: α = 0.10 **Steps in Statistical Analysis:** 1. **Hypotheses Formulation:** - **Null Hypothesis (H₀):** Population mean test score is the same in both settings. - **Alternative Hypothesis (H₁):** Population mean test score differs between settings. 2. **Test Selection:** - A suitable statistical test needs to be chosen for this comparative analysis. 3. **Calculation Requirements:** - **Test Statistic**: To be calculated (enter answer to 3 decimal places). - **P-value**: To be calculated (enter answer to 4 decimal places). 4. **Decision Criteria:** - Compare p-value with α (0.10) to determine statistical significance. 5. **Conclusion Determination:** - Decide to accept or reject the null hypothesis based on test results. 6. **Final Conclusion Options:** - **Option 1**: Results are statistically significant, suggesting a difference in performance settings. - **Option 2**: Results are not statistically significant, suggesting no difference. - **Option 3**: Results indicate no difference in average scores for the students. - **Option 4**: Results not statistically significant, suggesting equality in performance. This study aims to provide insights on whether exam environments impact student performance and guide instructional strategies accordingly.
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