Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 18 subjects had a mean wake time of 102.0 min. After​ treatment, the 18 subjects had a mean wake time of 74.7 min and a standard deviation of 22.7 min. Assume that the 18 sample values appear to be from a normally distributed population and construct a 99​% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 102.0 min before the​ treatment? Does the drug appear to be​ effective?

Construct the 99​% confidence interval estimate of the mean wake time for a population with the treatment.   

_____< μ < ____

min

​(Round to one decimal place as​ needed.)

Answer 1

t critical value at 0.01 level with 17 df = 2.898

99% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

74.7 - 2.898 * 22.7 / sqrt(18) < < 74.7 + 2.898 * 22.7 / sqrt(18)

59.2 < < 90.2

Since 102.0 not lies in confidence interval, the drug appear to be effective.