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,

26

subjects had a mean wake time of

95.6

min and a standard deviation of

42.6

min. Assume that the

26

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?

Answer 1

Solution :

Given that,

s = 42.6

s² = 1814.76

n = 26

Degrees of freedom = df = n - 1 = 26 - 1 = 25

At 90% confidence level the ² value is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

1 - / 2 = 1 - 0.05 = 0.95

²_L = ²_/2,df = 37.652

²_R = ²_{1 - /2,df} = 14.611

The 90% confidence interval for is,

(n - 1)s² / ²_/2 < < (n - 1)s² / ²_{1 - /2}

25 * 1814.76 / 37.652 < < 25 * 1814.76 / 14.611

34.71 < < 55.72

(34.71 , 55.72)

The treatment is​ not effective .