MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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# Confidence Interval and Point Estimate Calculation

## Scenario
As a researcher in a hospital, you are testing a new tranquilizer. You have collected data from a random sample of 8 patients regarding the duration of the drug's effectiveness. The times recorded (in hours) are as follows:

| Hours |
|-------|
| 2.8   |
| 2.2   |
| 2.3   |
| 2.5   |
| 2.7   |
| 3.0   |
| 2.5   |
| 2.6   |

## Questions

1. **Point Estimate Calculation**  
   What is a point estimate for the population mean length of time? (Round your answer to 2 decimal places)

   - Input box for the answer

2. **Requirements for Confidence Interval**  
   What must be true in order to construct a confidence interval in this situation?

   - Dropdown menu for selecting the answer

3. **Confidence Interval Construction**  
   Construct a 98% confidence interval for the population mean length of time. (Round upper and lower bounds to 2 decimal places)

   - Two input boxes for the lower and upper bounds

4. **Understanding Confidence Level**  
   What does it mean to be "98% confident" in this problem?

   - Options:
     - 98% of all confidence intervals found using this same sampling technique will contain the population mean time.
     - There is a 98% chance that the confidence interval contains the sample mean time.
     - The confidence interval contains 98% of all sample times.
     - 98% of all times will fall within this interval.

5. **Company Statement**  
   Suppose the company releases a statement that the mean time for all patients is 2 hours. Is this possible?

   - Dropdown menu for selecting the answer

- **Submit Button** for question submission

## Additional Notes
- For each step, ensure calculations are accurate.
- Use appropriate statistical methods for confidence interval estimation.
- Interpret the results clearly to understand the implications of the experiment findings.
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Transcribed Image Text:# Confidence Interval and Point Estimate Calculation ## Scenario As a researcher in a hospital, you are testing a new tranquilizer. You have collected data from a random sample of 8 patients regarding the duration of the drug's effectiveness. The times recorded (in hours) are as follows: | Hours | |-------| | 2.8 | | 2.2 | | 2.3 | | 2.5 | | 2.7 | | 3.0 | | 2.5 | | 2.6 | ## Questions 1. **Point Estimate Calculation** What is a point estimate for the population mean length of time? (Round your answer to 2 decimal places) - Input box for the answer 2. **Requirements for Confidence Interval** What must be true in order to construct a confidence interval in this situation? - Dropdown menu for selecting the answer 3. **Confidence Interval Construction** Construct a 98% confidence interval for the population mean length of time. (Round upper and lower bounds to 2 decimal places) - Two input boxes for the lower and upper bounds 4. **Understanding Confidence Level** What does it mean to be "98% confident" in this problem? - Options: - 98% of all confidence intervals found using this same sampling technique will contain the population mean time. - There is a 98% chance that the confidence interval contains the sample mean time. - The confidence interval contains 98% of all sample times. - 98% of all times will fall within this interval. 5. **Company Statement** Suppose the company releases a statement that the mean time for all patients is 2 hours. Is this possible? - Dropdown menu for selecting the answer - **Submit Button** for question submission ## Additional Notes - For each step, ensure calculations are accurate. - Use appropriate statistical methods for confidence interval estimation. - Interpret the results clearly to understand the implications of the experiment findings.
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