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, 23 subjects had a mean wake time of 96.9 min and a standard deviation of 40.9 min. Assume that the 23 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 < o < min

Answer 1

Solution :

Given that,

s = 40.9

s2 = 1672.81

n = 23

Degrees of freedom = df = n - 1 = 23 - 1 = 22

At 95% confidence level the 2 value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

2L = 2/2,df =36.7807

2R = 21 - /2,df = 10.9823

The 95% confidence interval for is,

(n - 1)s2 / 2/2 < < (n - 1)s2 / 21 - /2

  (22)1672.81 /36.7807< < (22 )1672.81 / 10.9823

31.6319 < < 57.8879

( 31.6319 , 57.8879 ) min