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 103.0 min. After​ treatment, the 18 subjects had a mean wake time of 78.4 min and a standard deviation of 20.7 min. Assume that the 18 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 103.0 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. nothing minless than muless thannothing min ​(Round to one decimal place as​ needed.)

Answer 1

Given,

After​ treatment, the 18 subjects had a mean wake time of 78.4 min and a standard deviation of 20.7 min.

i.e Sample size : n= 18

Sample mean : = 78.4

Sample standard deviation : s= 20.7

Degrees of freedom = n-1 = 18-1 = 17

Confidence interval estimate for population mean: when population standard deviation is not known

Confidence Level :	95
	0.05
/2	0.025
	2.1098

95 ​% confidence interval estimate of the mean wake time for a population with drug treatments

95 ​% confidence interval estimate of the mean wake time for a population with drug treatments (68.1062, 88.6938)

i.e

68.1062 min < < 88.6938 min

As, Before​ treatment, mean wake time of 18 subjects : 103.0 min is much less than the upper confidence limit of the: 95 ​% confidence interval estimate of the mean wake time for a population with drug treatments; which suggest that the drug treatment is effective.