A clinical trial was conducted to test the effectiveness of a drug for treating

Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 15 subjects had a mean wake time of 102.0 min. After treatment, the 15 subjects had a mean wake time of 77.1 min and a standard deviation of 41.6 min. Assume that the 15 sample values appear to be from a normally distributed population and construct a 95% 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 95% confidence interval estimate of the mean wake time for a population with the treatment. (Round to one decimal place as needed.)

Explanation / Answer

Given : Sample Mean = 77.1, s = 41.6, n = 15, Alpha = 0.0

Since population standard deviation is unknown, the tcritical (2 tail) for Alpha = 0.05, for df = n -1 = 14, is 2.1448

The Confidence Interval is given by Sample Mean ± ME, where

ME = tcritical * s/Sqrt(n) = 2.1448 * 41.6/{sqrt(15)} = 23.037

The Lower Limit = 77.1 - 23.037 = 54.063. Rounding to 1 decimal place = 54.1

The Upper Limit = 77.1 + 23.037 = 100.13. Rounding to 1 decimal place = 100.1

The Confidence Interval is 54.1 < Mu < 100.1

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