Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 23 subjects had a mean wake time of 100.0 min. After​ treatment, the 23 subjects had a mean wake time of 90.1 min and a standard deviation of 24.4 min. Assume that the 23 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 100.0 min before the​ treatment? Does the drug appear to be​ effective?

Answer 1

t critical value at 0.01 level with 22 df = 2.819

99% confidence interval for is

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

90.1 - 2.819 * 24.4 / sqrt(23) < < 90.1 + 2.819 * 24.4 / sqrt(23)

75.76 < < 104.44

99% CI is (75.76 , 104.44)

Since claimed mean 100 min lies in this confidence interval, we do not have sufficient evidence

to support the clai,

The drug does not appear to be effective.