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,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

Answer 1

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