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
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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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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