Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 103.0 min. After​ treatment, the 13 subjects had a mean wake time of 80.4 min and a standard deviation of 22.3 min. Assume that the 13 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.

Answer 1

Solution:

Given:

Sample mean = = 80.4

Sample Standard deviation = s = 22.3

Sample size = n = 13

Degrees of freedom = df=13−1=12

The significance level is α=0.1.

The critical t-value is.

tc = 1.782 ...Using excel formula, =TINV(0.1,12)

90% confidence interval for population mean is,

Calculation:

The confidence interval is 69.377 < < 91.423

The 90% confidence interval for mean wake time is (69.377 < < 91.423), which is less than 103.0 minutes.

Therefore, the result suggest that due to drug treatment , mean wake time becomes less than 103.0 min.

Hence, drug appear to be effective.

Done