Estimating Population Standard Deviation or Va

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,

17

subjects had a mean wake time of

90.8

min and a standard deviation of

41.6

min. Assume that the

17

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?

Answer 1

Confidence Interval for Standard Deviation:

sqrt( (n-1)*s^2/ chi-square alpha/2, n-1 DOF) < sigma < sqrt( (n-1)*s^2/ chi-square 1-alpha/2, n-1 DOF)

where n = 17, s = 41.6, alpha = 0.01, DOF = degrees of freedom