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, 12 subjects had a mean wake time of 92.3 min and a standard deviation of 41.6 min. Assume that the 12 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? Find the confidence interval estimate.

_____ min < σ < ______min

min

Answer 1

Solution :  

Given that,

c = 98% = 0.98

n = 12

s = 41.6

d.f. = n - 1 = 12 - 1 = 11

At 98% confidence level the is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.01 and 1 - ( / 2) = 0.99

Now , using chi square table ,

_/2,df = _0.01,11   = 24.725

_{1- /2,df} = _0.99,11 = 3.0535

The 98% confidence interval for is,

41.6 [(12 - 1 ) / 24.725] < < 41.6[(12 - 1 ) / 3.0535]

27.75 < < 78.96

Answer :

27.75 min < < 78.96 min