Question

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the​ drug, 26 subjects had a mean wake time of 96.1 min and a standard deviation of 41.2 min. Assume that the 26 sample values appear to be from a normally distributed population and construct a 95​% 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.

___min < sigma <___min

​(Round to two decimal places as​ needed.)

Answer 1

We have given here,                      
                      
Sample variance =1697.44              
Sample standard deviation=41.2          
Sample size =26              
                      
Degree of freedom =n-1=   25          
Level of significance given =0.05          
Chi square critical value for lower tail=13.120      
                      
Chi square critical value for upper tail=40.646      
                      
We can use here confidence interval formula for population standard deviation  

=(32.31, 56.87)                  
                      
                      
                      
  
                      
Lower confidence limit for population standard deviation=32.31
                      
Upper confidence limit for Population standard deviation=56.87