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, 24 subjects had a mean wake time of 96.1 min and a standard deviation of 42.5 min. Assume that the 24 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?

Answer 1

Here s = 42.5 and n = 24
df = 24 - 1 = 23

α = 1 - 0.98 = 0.02
The critical values for α = 0.02 and df = 23 are Χ^2(1-α/2,n-1) = 10.196 and Χ^2(α/2,n-1) = 41.638

CI = (sqrt(23*42.5^2/41.638) , sqrt(23*42.5^2/10.196))
CI = (31.587 , 63.8319)

The calculated CI does not show any result about the effectiveness of the treatment.