Do students perform worse when they take an exam alone than 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 70 87 76 78 74 80 77 65 67 83 78 82 73 88 77 71 Alone Classroom Assume a Normal distribution. What can be concluded at the the a = 0.05 level of significance level of significance? For this study, we should use t-test for the difference between two dependent population mean: a. The null and alternative hypotheses would be: Ho: μd 0 H₁: 0 ud (please enter a decimal) (Please enter a decimal) b. The test statistic show your answer to 3 decimal places.) c. The p-value = (please (Please show your answer to 4 decimal places.
Do students perform worse when they take an exam alone than 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 70 87 76 78 74 80 77 65 67 83 78 82 73 88 77 71 Alone Classroom Assume a Normal distribution. What can be concluded at the the a = 0.05 level of significance level of significance? For this study, we should use t-test for the difference between two dependent population mean: a. The null and alternative hypotheses would be: Ho: μd 0 H₁: 0 ud (please enter a decimal) (Please enter a decimal) b. The test statistic show your answer to 3 decimal places.) c. The p-value = (please (Please show your answer to 4 decimal places.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![### Exam Performance Analysis: Solitary vs. Classroom Settings
**Research Question:**
Do students perform worse when they take an exam alone than when they take an exam in a classroom setting?
**Study Design:**
Eight students were given two tests of equal difficulty. Each student took one test in a solitary room and the other in a room filled with other students. The results are shown in the table below.
#### Exam Scores
| | **Alone** | **Classroom** |
|-----------|-----------|---------------|
| **Student 1** | 70 | 67 |
| **Student 2** | 87 | 83 |
| **Student 3** | 76 | 78 |
| **Student 4** | 78 | 82 |
| **Student 5** | 74 | 73 |
| **Student 6** | 80 | 88 |
| **Student 7** | 77 | 77 |
| **Student 8** | 65 | 71 |
**Statistical Test:**
Assume a Normal distribution. We aim to conclude at the \( \alpha = 0.05 \) level of significance.
For this study, we will use a *t-test for the difference between two dependent population means*.
### Steps for Hypothesis Testing:
**a. Null and Alternative Hypotheses:**
- Null hypothesis (\( H_0 \)): \( \mu_d = 0 \)
- Alternative hypothesis (\( H_1 \)): \( \mu_d < 0 \)
Where:
- \( \mu_d \) is the mean difference between the scores in the two settings.
**b. Test Statistic:**
Calculate the test statistic \( t \):
\[ t = \text{(please show your answer to 3 decimal places)} \]
**c. p-value:**
Calculate the p-value:
\[ \text{p-value} = \text{(please show your answer to 4 decimal places)} \]
### Conclusion:
Based on the calculated test statistic and p-value, determine whether to reject the null hypothesis. This will allow us to conclude whether students indeed perform worse when taking an exam alone compared to taking it in a classroom setting.
---
**Explanation of the Graph:**
The table provided lists](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff1914c56-6f05-4bb9-a00f-e50742b81a7f%2Fcc673736-6783-458b-ab93-4b302e964124%2Fs43vk4a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exam Performance Analysis: Solitary vs. Classroom Settings
**Research Question:**
Do students perform worse when they take an exam alone than when they take an exam in a classroom setting?
**Study Design:**
Eight students were given two tests of equal difficulty. Each student took one test in a solitary room and the other in a room filled with other students. The results are shown in the table below.
#### Exam Scores
| | **Alone** | **Classroom** |
|-----------|-----------|---------------|
| **Student 1** | 70 | 67 |
| **Student 2** | 87 | 83 |
| **Student 3** | 76 | 78 |
| **Student 4** | 78 | 82 |
| **Student 5** | 74 | 73 |
| **Student 6** | 80 | 88 |
| **Student 7** | 77 | 77 |
| **Student 8** | 65 | 71 |
**Statistical Test:**
Assume a Normal distribution. We aim to conclude at the \( \alpha = 0.05 \) level of significance.
For this study, we will use a *t-test for the difference between two dependent population means*.
### Steps for Hypothesis Testing:
**a. Null and Alternative Hypotheses:**
- Null hypothesis (\( H_0 \)): \( \mu_d = 0 \)
- Alternative hypothesis (\( H_1 \)): \( \mu_d < 0 \)
Where:
- \( \mu_d \) is the mean difference between the scores in the two settings.
**b. Test Statistic:**
Calculate the test statistic \( t \):
\[ t = \text{(please show your answer to 3 decimal places)} \]
**c. p-value:**
Calculate the p-value:
\[ \text{p-value} = \text{(please show your answer to 4 decimal places)} \]
### Conclusion:
Based on the calculated test statistic and p-value, determine whether to reject the null hypothesis. This will allow us to conclude whether students indeed perform worse when taking an exam alone compared to taking it in a classroom setting.
---
**Explanation of the Graph:**
The table provided lists
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