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 103.0 min. After treatment, the 22 subjects had a mean wake time of 98.3 min and a standard deviation of 23.1 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 103.0 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. min<< min (Round to one decimal place as needed.)

Answer 1

With treatment, the mean wake time, $\mu$ = 98.3 min

Standard deviation of the wake time, $\sigma$ = 23.1 min

n = 22

Corresponding to 90% confidence interval and n = 22, the critical t score = 1.721

Thus, the required 90% confidence interval

= $(98.3 - 1.721*\frac{23.1}{\sqrt{22}}, 98.3+1.721*\frac{23.1}{\sqrt{22}})$

= (89.8, 106.8)

89.8 min < $\mu$ < 106.8 min

The 90% confidence interval estimate of the mean wake time for a population with treatment contains the mean wake time of 103 min before the treatment.

Thus, the drug does not appear to be effective