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 77.2 min and a standard deviation of 22.6 min. Assume that the 22 sample values appear to be from a normally distributed population and construct a 99​% 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?

What does the result suggest about the mean wake time of 103.0 min before the​ treatment? Does the drug appear to be​ effective?

(Options in parenthesis are the possible answers)

The confidence interval (does not include, includes) the mean wake time of 103.0 min before the​ treatment, so the means before and after the treatment (are different, could be the same) This result suggests that the drug treatment (has, does not have) a significant effect.

Answer 1

(a)

SE = s/$\sqrt{n}$

= 22.6/$\sqrt{22}$ = 4.8183

$\alpha$ = 0.01

ndf = n - 1 = 22 - 1= 21

From Table critical values of t = $\pm$ 2.8314

Confidence Interval:

77.2 $\pm$ (2.8314 X 4.8183)

= 77.2 $\pm$ 13.6426

= (63.5574 ,90.8426)

So,

Confidence Interval:

63.5574 < $\mu$ < 90.8426

(b)

The confidence interval does not include the mean wake up time of 103.0 min before the treatment so, the means before and after the treatment are different. This result suggests that the rug treatment has significant effect.