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 100.0 min. After​ treatment, the 18 subjects had a mean wake time of 79.2 min and a standard deviation of 41.1 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 100.0 min before the​ treatment? Does the drug appear to be​ effective?

Answer 1

The 90% confidence interval estimate for the mean wake time after the drug treatment is 63.6 to 94.8 minutes. This suggests a significant reduction in the mean wake time from the pre-treatment value of 100.0 minutes, indicating the potential effectiveness of the drug.

Step-by-step explanation:

The construction of a 90% confidence interval involves calculating the margin of error around the sample mean. In this case, the interval (63.6 to 94.8 minutes) suggests that we can be 90% confident that the true population mean wake time after the drug treatment falls within this range. The lower limit being below the pre-treatment mean (100.0 minutes) implies a reduction in wake time.

The standard deviation of 41.1 minutes indicates variability in the sample, but the confidence interval's narrow width suggests a relatively precise estimate. The fact that the entire interval is below the pre-treatment mean of 100.0 minutes implies a consistent improvement. Therefore, the drug appears to be effective in reducing wake time in older subjects with insomnia.

It's crucial to note that statistical significance alone does not guarantee clinical significance, and other factors such as side effects and long-term effects should be considered. Nonetheless, based on the provided data and confidence interval, there is evidence to suggest a positive impact of the drug on the mean wake time of the population under study.