d. The p-value is ? e. Based on this, we should Select an answer O the null hypothesis. f. Thus, the final conclusion is that ... The results are statistically insignificant at a = 0.10, so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye. The results are statistically significant at a = 0.10, so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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NEED HELP WITH: D,E, F

**Assume a Normal distribution. What can be concluded at the α = 0.10 level of significance?**

For this study, we should use [Select an answer].

a. The null and alternative hypotheses would be:

\[ H_0: \] [Select an answer] [ ? ] [Select an answer] [ (please enter a decimal) ]

\[ H_1: \] [Select an answer] [ ? ] [Select an answer] [ (Please enter a decimal) ]

b. The test statistic [ ? ] = [ _____ ] (please show your answer to 3 decimal places.)

c. The p-value = [ _____ ] (Please show your answer to 4 decimal places.)

d. The p-value is [ ? ] α

e. Based on this, we should [Select an answer] the null hypothesis.

f. Thus, the final conclusion is that ...

- ○ The results are statistically insignificant at α = 0.10, so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye.

- ○ The results are statistically significant at α = 0.10, so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye.

- ○ The results are statistically significant at α = 0.10, so there is sufficient evidence to conclude that the eight volunteers completed the course slower on average with the patch over the right eye compared to the left eye.

- ○ The results are statistically insignificant at α = 0.10, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye.
Transcribed Image Text:**Assume a Normal distribution. What can be concluded at the α = 0.10 level of significance?** For this study, we should use [Select an answer]. a. The null and alternative hypotheses would be: \[ H_0: \] [Select an answer] [ ? ] [Select an answer] [ (please enter a decimal) ] \[ H_1: \] [Select an answer] [ ? ] [Select an answer] [ (Please enter a decimal) ] b. The test statistic [ ? ] = [ _____ ] (please show your answer to 3 decimal places.) c. The p-value = [ _____ ] (Please show your answer to 4 decimal places.) d. The p-value is [ ? ] α e. Based on this, we should [Select an answer] the null hypothesis. f. Thus, the final conclusion is that ... - ○ The results are statistically insignificant at α = 0.10, so there is statistically significant evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is equal to the population mean time to complete the obstacle course with a patch over the left eye. - ○ The results are statistically significant at α = 0.10, so there is sufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye. - ○ The results are statistically significant at α = 0.10, so there is sufficient evidence to conclude that the eight volunteers completed the course slower on average with the patch over the right eye compared to the left eye. - ○ The results are statistically insignificant at α = 0.10, so there is insufficient evidence to conclude that the population mean time to complete the obstacle course with a patch over the right eye is greater than the population mean time to complete the obstacle course with a patch over the left eye.
### Exercise: Analyzing Completion Times with Eye Patches

**Objective:**  
Determine if the average time to complete an obstacle course is longer when a patch is placed over the right eye compared to the left eye.

**Study Setup:**  
Thirteen volunteers completed two runs of an obstacle course, one with a patch over each eye. The completion times were recorded:

| Time to Complete the Course (seconds) |   |
|--------------------------------------|---|
| **Right Eye Covered**                | 46, 50, 42, 42, 50, 47, 46, 42 |
| **Left Eye Covered**                 | 45, 48, 41, 41, 48, 45, 46, 43 |

**Statistical Analysis Steps:**

1. **Assumptions and Distribution:**
   - Assume a normal distribution of completion times.

2. **Significance Level:**
   - Use an alpha level (\(\alpha\)) of 0.10 for the test.

3. **Hypotheses:**
   - The null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)) need to be defined for this test.

4. **Statistical Test:**
   - Choose an appropriate test (e.g., t-test) to analyze the data.

5. **Calculations:**
   a. **Test Statistic:** 
      - Calculate, showing results to three decimal places.
   b. **P-value:** 
      - Determine and present the p-value, showing four decimal places.

6. **Conclusion:**
   - Compare the p-value with \(\alpha\) to decide whether to reject or fail to reject the null hypothesis.
   - Provide a final conclusion based on the analysis, whether the results are statistically significant.

**Final Statements (Choose one):**
- **Insignificant Results:** The results are statistically insignificant at \(\alpha = 0.10\), indicating insufficient evidence to conclude a difference in mean completion time between the right and left eye patches.
  
- **Significant Results:** The results are statistically significant at \(\alpha = 0.10\), providing sufficient evidence to conclude a difference in mean completion time between the right and left eye patches.

Use this analysis to draw conclusions about the effect of eye patch placement on the obstacle course completion time.
Transcribed Image Text:### Exercise: Analyzing Completion Times with Eye Patches **Objective:** Determine if the average time to complete an obstacle course is longer when a patch is placed over the right eye compared to the left eye. **Study Setup:** Thirteen volunteers completed two runs of an obstacle course, one with a patch over each eye. The completion times were recorded: | Time to Complete the Course (seconds) | | |--------------------------------------|---| | **Right Eye Covered** | 46, 50, 42, 42, 50, 47, 46, 42 | | **Left Eye Covered** | 45, 48, 41, 41, 48, 45, 46, 43 | **Statistical Analysis Steps:** 1. **Assumptions and Distribution:** - Assume a normal distribution of completion times. 2. **Significance Level:** - Use an alpha level (\(\alpha\)) of 0.10 for the test. 3. **Hypotheses:** - The null hypothesis (\(H_0\)) and the alternative hypothesis (\(H_1\)) need to be defined for this test. 4. **Statistical Test:** - Choose an appropriate test (e.g., t-test) to analyze the data. 5. **Calculations:** a. **Test Statistic:** - Calculate, showing results to three decimal places. b. **P-value:** - Determine and present the p-value, showing four decimal places. 6. **Conclusion:** - Compare the p-value with \(\alpha\) to decide whether to reject or fail to reject the null hypothesis. - Provide a final conclusion based on the analysis, whether the results are statistically significant. **Final Statements (Choose one):** - **Insignificant Results:** The results are statistically insignificant at \(\alpha = 0.10\), indicating insufficient evidence to conclude a difference in mean completion time between the right and left eye patches. - **Significant Results:** The results are statistically significant at \(\alpha = 0.10\), providing sufficient evidence to conclude a difference in mean completion time between the right and left eye patches. Use this analysis to draw conclusions about the effect of eye patch placement on the obstacle course completion time.
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