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 105.0 min. After​ treatment, the 15 subjects had a mean wake time of 101.6 min and a standard deviation of 21.5 min. Assume that the 15 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 105.0 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.

Answer 1

(a)

= 101.6

s = 21.5

n = 15

df = 15 - 1 = 14

= 0.10

From Table, critical values of t = 1.761

Confidence Interval:

So,

Answer is:

(91.822, 111.378)

(b)

Since not all values in the confidence interval (91.822, 111.378) are less than 105.0, we conclude:

the drug does not appear to be​ effective

(c)

the 90​% confidence interval estimate of the mean wake time for a population with the treatment. is given by:

(91.822, 111.378)