Statistics Question

Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 22 subjects had a mean wake time of 101.0

min. After​ treatment, the 22 subjects had a mean wake time of 96.5 min and a standard deviation of 20.6

min. Assume that the 22 sample values appear to be from a normally distributed population and construct a

90​% 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?

Construct the 90​% confidence interval estimate of the mean wake time for a population with the treatment.

Answer 1

90% confidence level corresponds to alpha = 0.1, so alpha/2 = 0.05

For sample size of 22, number of degrees of freedom is 21. critical t for confidence interval for alpha/2 = 0.05 and DOF = 21 is 1.721

CI for mean is mean +/- t-critical * standard deviation/square root(sample size) =

96.5 +/- 1.721 * 20.6/sqrt(21) = (88.76, 104.24)

The mean wake time of 101 before the treatment is within the 90% confidence interval for plausible wake times for after the treatment, which would indicate that we cannot conclude the treatment is effective at the significance level of 0.1.