In: Statistics and Probability
A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug,13 subjects had a mean wake time of 90.4 min and a standard deviation of 44.8 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 90% 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
Solution :
Given that,
c = 0.90
s = 44.8
n = 13
At 90% confidence level the is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
/2,df = 0.05,12 = 21.03
and
1- /2,df = 0.95,12 = 5.23
2L = 2/2,df = 21.03
2R = 21 - /2,df = 5.23
The 90% confidence interval for is,
s (n-1) / /2,df < < s (n-1) / 1- /2,df
44.8 ( 13 - 1 ) / 21.03 < < 44.8 ( 13 - 1 ) / 5.23
33.84 min < < 67.89 min