Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 25 subjects had a mean wake time of 101.0 min. After​ treatment, the 25 subjects had a mean wake time of 75.9 min and a standard deviation of 20.7 min. Assume that the 25 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 101.0 min before the​ treatment? Does the drug appear to be​ effective?

Answer 1

t critical value at 0.01 level with 24 df = 2.797

99% confidence interval for $\mu$ is

$\bar{x}$ - t * S / sqrt(n) < $\mu$ < $\bar{x}$ + t * S / sqrt(n)

75.9 - 2.797 * 20.7 / sqrt(25) < $\mu$ < 75.9 + 2.797 * 20.7 / sqrt(25)

64.32 < $\mu$ < 87.78

99% CI is (64.32 , 87.78)

Since claimed mean 101.0 is outside the confidence interval, we have sufficient evidence to

reject H0.

We conclude at 0.01 level that the drug appear to be effective