A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 19 subjects had a mean wake time of 100.0 min. After treatment, the 19 subjects had a mean wake time of 72.6 min and a standard deviation of 22.8 min. Assume that the 19 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 100.0 min before the treatment? Does the drug appear to be effective?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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**Description of the Educational Content:**

A clinical trial was conducted to examine the effectiveness of a drug for treating insomnia in older subjects. The study involved 19 subjects. Before the treatment, these subjects had a mean wake time of 100.0 minutes. After the treatment, the mean wake time was reduced to 72.6 minutes, with a standard deviation of 22.8 minutes.

**Objective:**
To determine the effect of the drug treatment on mean wake time by constructing a 99% confidence interval for the mean wake time of a population with the treatment.

**Instructions:**

1. **Construct the 99% Confidence Interval:**
   - Calculate the interval estimate for the mean wake time for the population receiving the treatment.
   - Formula: \( \min < \mu < \min \)
   - Round the result to one decimal place as needed.

2. **Analysis:**
   - If the confidence interval excludes the mean wake time of 100.0 minutes before the treatment, determine if there is a significant effect.
   - Consider whether the drug appears to be effective based on this confidence interval.

3. **Answer Boxes:**
   - Fill in the confidence interval values and the conclusion on the drug's effectiveness.
   - The confidence interval [select option] the mean wake time of 100.0 min before the treatment, implying [select option] effect.

**Conclusion:**
- Analyze and input whether the drug treatment had a significant impact based on the confidence interval findings.
Transcribed Image Text:**Description of the Educational Content:** A clinical trial was conducted to examine the effectiveness of a drug for treating insomnia in older subjects. The study involved 19 subjects. Before the treatment, these subjects had a mean wake time of 100.0 minutes. After the treatment, the mean wake time was reduced to 72.6 minutes, with a standard deviation of 22.8 minutes. **Objective:** To determine the effect of the drug treatment on mean wake time by constructing a 99% confidence interval for the mean wake time of a population with the treatment. **Instructions:** 1. **Construct the 99% Confidence Interval:** - Calculate the interval estimate for the mean wake time for the population receiving the treatment. - Formula: \( \min < \mu < \min \) - Round the result to one decimal place as needed. 2. **Analysis:** - If the confidence interval excludes the mean wake time of 100.0 minutes before the treatment, determine if there is a significant effect. - Consider whether the drug appears to be effective based on this confidence interval. 3. **Answer Boxes:** - Fill in the confidence interval values and the conclusion on the drug's effectiveness. - The confidence interval [select option] the mean wake time of 100.0 min before the treatment, implying [select option] effect. **Conclusion:** - Analyze and input whether the drug treatment had a significant impact based on the confidence interval findings.
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