A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 25 subjects had a mean wake time of 102.0 min. After treatment, the 25 subjects had a mean wake time of 75.7 min and a standard deviation of 21.1 min. Assume that the 25 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 102.0 min before the treatment? Does the drug appear to be effective? Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment. O min

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**Clinical Trial Analysis: Insomnia Drug Effectiveness**

A clinical trial was conducted to evaluate the effectiveness of a drug for treating insomnia in older subjects. 

- **Before Treatment:** 25 subjects had a mean wake time of 102.0 minutes.
- **After Treatment:** The same 25 subjects had a mean wake time of 75.7 minutes, with a standard deviation of 21.1 minutes.

Assuming the 25 sample values are from a normally distributed population, a 99% confidence interval estimate of the mean wake time for a population with drug treatment needs to be constructed. 

**Objective:** Determine if the result suggests a significant reduction in the mean wake time, implying the drug's effectiveness.

**Task:** Construct the 99% confidence interval for the mean wake time for a population with the treatment. 

\[ \text{min} < \mu < \text{min} \]

*Note: Round to one decimal place as needed.*

This analysis will help conclude whether the drug significantly reduces wake time compared to the baseline (pre-treatment wake time of 102.0 minutes). 

**Conclusion Criteria:** 
- Assess if the interval suggests a reduction below the baseline mean wake time.
- Determine if the drug appears effective based on this statistical analysis.
Transcribed Image Text:**Clinical Trial Analysis: Insomnia Drug Effectiveness** A clinical trial was conducted to evaluate the effectiveness of a drug for treating insomnia in older subjects. - **Before Treatment:** 25 subjects had a mean wake time of 102.0 minutes. - **After Treatment:** The same 25 subjects had a mean wake time of 75.7 minutes, with a standard deviation of 21.1 minutes. Assuming the 25 sample values are from a normally distributed population, a 99% confidence interval estimate of the mean wake time for a population with drug treatment needs to be constructed. **Objective:** Determine if the result suggests a significant reduction in the mean wake time, implying the drug's effectiveness. **Task:** Construct the 99% confidence interval for the mean wake time for a population with the treatment. \[ \text{min} < \mu < \text{min} \] *Note: Round to one decimal place as needed.* This analysis will help conclude whether the drug significantly reduces wake time compared to the baseline (pre-treatment wake time of 102.0 minutes). **Conclusion Criteria:** - Assess if the interval suggests a reduction below the baseline mean wake time. - Determine if the drug appears effective based on this statistical analysis.
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