A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug, 21 subjects had a mean wake time of 96.9 min and a standard deviation of 42.3 min. Assume that the 21 sample values appear to be from a normally distributed population and construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is effective? Find the confidence interval estimate. O min

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### Clinical Trial Analysis: Insomnia Treatment

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. Following treatment with the drug, 21 subjects had a mean wake time of 96.9 minutes and a standard deviation of 42.3 minutes. Assume that the 21 sample values appear to be from a normally distributed population. 

The task is to construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments, and determine if the results indicate whether the treatment is effective.

**Steps to Find the Confidence Interval Estimate:**

1. **Identify the Parameters:**
   - Sample size (\( n \)) = 21
   - Sample mean (\( \bar{x} \)) = 96.9 minutes
   - Standard deviation (\( s \)) = 42.3 minutes
   - Confidence level = 98%

2. **Formulate the Confidence Interval:**
   - The confidence interval for the standard deviation can be calculated using chi-square distribution.

3. **Calculate Using Chi-Square Distribution:**
   - Calculate the chi-square values for 98% confidence level, with degrees of freedom (\( n - 1 \)) = 20.

4. **Result Interpretation:**
   - Evaluate the computed confidence interval to understand if the treatment significantly changes the wake times, thus assessing the effectiveness of the drug.

**Interactive Element:**

- **Input Field:**
  - Enter your answer in the edit fields and then click "Check Answer" to verify.
  
- **Progress Tracker:**
  - Track how many parts of the problem you have completed with the progress bar displayed below the input field.

**Note:** Be sure to round your final answers to two decimal places as needed.

This problem requires statistical analysis skills and an understanding of confidence intervals using chi-square distribution to evaluate drug treatment effectiveness in clinical trials.
Transcribed Image Text:### Clinical Trial Analysis: Insomnia Treatment A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. Following treatment with the drug, 21 subjects had a mean wake time of 96.9 minutes and a standard deviation of 42.3 minutes. Assume that the 21 sample values appear to be from a normally distributed population. The task is to construct a 98% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments, and determine if the results indicate whether the treatment is effective. **Steps to Find the Confidence Interval Estimate:** 1. **Identify the Parameters:** - Sample size (\( n \)) = 21 - Sample mean (\( \bar{x} \)) = 96.9 minutes - Standard deviation (\( s \)) = 42.3 minutes - Confidence level = 98% 2. **Formulate the Confidence Interval:** - The confidence interval for the standard deviation can be calculated using chi-square distribution. 3. **Calculate Using Chi-Square Distribution:** - Calculate the chi-square values for 98% confidence level, with degrees of freedom (\( n - 1 \)) = 20. 4. **Result Interpretation:** - Evaluate the computed confidence interval to understand if the treatment significantly changes the wake times, thus assessing the effectiveness of the drug. **Interactive Element:** - **Input Field:** - Enter your answer in the edit fields and then click "Check Answer" to verify. - **Progress Tracker:** - Track how many parts of the problem you have completed with the progress bar displayed below the input field. **Note:** Be sure to round your final answers to two decimal places as needed. This problem requires statistical analysis skills and an understanding of confidence intervals using chi-square distribution to evaluate drug treatment effectiveness in clinical trials.
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