A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 102.0 min. After​ treatment, the 13 subjects had a mean wake time of 79.4 min and a standard deviation of 21.2 min. Assume that the 13 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 102.0 min before the​ treatment? Does the drug appear to be​ effective?

Accepted Solution

Answer:Confidence interval:  11.5 < µ < 30.9Read below to see conclusion:Step-by-step explanation:n = 13, x = 79.4, s = 21.2, Z = 1.645 (z score for a confidence interval with 90% confidence)Use the formula to find the error:  E = Z(s/√n)We have: E = 1.645(21.2/√13) = 9.7Now construct the confidence interval:x - E < µ < x + E21.2 - 9.7 < µ < 21.2 + 9.711.5 < µ < 30.9Yes, the drug appears to be effective because the estimated wake time for a population using this drug will be between 11.5 and 30.9 minutes.   The upper end of this interval is much lower than 102, so it appears as though the drug is effective.