A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 16 subjects had a mean wake time of 102.0 min. After treatment, the 16 subjects had a mean wake time of 95.2 min and a standard deviation of 20.4 min. Assume that the 16 sample values appear to be from a normally distributed population and construct a 95% 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 95% confidence interval estimate of the mean wake time for a population with the treatment. min <µ
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 16 subjects had a mean wake time of 102.0 min. After treatment, the 16 subjects had a mean wake time of 95.2 min and a standard deviation of 20.4 min. Assume that the 16 sample values appear to be from a normally distributed population and construct a 95% 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 95% confidence interval estimate of the mean wake time for a population with the treatment. min <µ
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:**Study on Drug Effectiveness for Insomnia in Older Subjects**
A clinical trial was conducted to evaluate a drug's effectiveness in treating insomnia among older individuals. Before the treatment, 16 subjects had a mean wake time of 102.0 minutes. After receiving the treatment, the same group of 16 subjects showed a reduced mean wake time of 95.2 minutes with a standard deviation of 20.4 minutes. The assumption was made that these 16 sample values are representative of a normally distributed population.
**Objective:**
To construct a 95% confidence interval estimate of the mean wake time for a population using the drug treatment. This estimate aims to determine whether the drug effectively reduced the mean wake time from 102.0 minutes that was recorded before the treatment. The core questions addressed are:
- What does the result imply about the mean wake time of 102.0 minutes before the treatment?
- Does the drug appear to be effective in reducing wake time?
**Task:**
Utilize statistical techniques to construct the 95% confidence interval for the mean wake time for the population subjected to the treatment.
**Formula:**
```
min < μ < max
```
(Please round to one decimal place as needed.)
Expert Solution
Step 1
Since population standard deviation is unknown, Use t-distribution to find t-critical value.
Find t-critical value:
Refer to t-distribution table OR use excel function "=T.INV.2T(0.05,15)" to find the critical value of t
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