Question

a clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. before treatment, 18 subjects had a mean wake time of 104.0 min. after treatment, the 18 subjects had a mean wake time of 83.1 min and a standard deviation of 22.7 min. assume that the 18 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 104.0 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.
73.8 min < μ < 92.4 min
(round to one decimal place as needed.)

what does the result suggest about the mean wake time of 104.0 min before the treatment? does the drug appear to be effective?
the confidence interval the mean wake time of 104.0 min before the treatment, so the means before and after the treatment this result suggests that the drug treatment an effect.

Explanation:

Step1: Analyze the confidence interval

The confidence interval for the mean wake - time after treatment is \(73.8\space min<\mu < 92.4\space min\). The value \(104.0\space min\) (mean wake - time before treatment) is not within this interval.

Step2: Compare the means

Since \(104.0\) is not in the interval \((73.8,92.4)\), the means before and after treatment are different.

Step3: Determine drug effectiveness

If the mean wake - time after treatment is lower (as the new mean's confidence interval is much lower than the pre - treatment mean), the drug appears to have an effect.

Answer:

The confidence interval does not include the mean wake time of \(104.0\space min\) before the treatment, so the means before and after the treatment are different. This result suggests that the drug treatment does have an effect.