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 90.8 min and a standard deviation of 43.4 min. Assume that the 24 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?

A) Find the confidence interval estimate.

B) Does the result indicate whether the treatment is​ effective?

Answer 1

Solution :  

A) Given that,

c = 95% = 0.95

s = 43.4

n = 24

d.f. = n - 1 = 24 - 1 = 23

= 1 - 0.95 = 0.05

/ 2 = 0.025

1 - ( / 2) = 0.975

Now , using chi square table ,

= _0.025,23 = 38.076

=  _0.975,23 = 11.689

The 98% confidence interval for is,

43.4  [(24 - 1 ) / 38.076] < < 43.4[(24 - 1 ) / 11.689]

Answer : 33.7309 < < 60.8786

B) from the results of above interval we can say that the treatment not effective.