Question

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment,

25

subjects had a mean wake time of

100.0

min. After​ treatment, the

25

subjects had a mean wake time of

96.7

min and a standard deviation of

21.8

min. Assume that the

25

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

100.0

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 :

degrees of freedom = n - 1 = 25 - 1 = 24

t/2,df = t0.05,24 = 1.711

Margin of error = E = t/2,df * (s /n)

= 1.711 * ( 21.8/ 25)

Margin of error = E = 7.5

The 90% confidence interval estimate of the population mean is,

- E < < + E

96.7 - 7.5 < < 96.7 + 7.5

( 89.2min. < < 104.2 min.)

The confidence interval include the mean wake time of 100.0 min.before the treatment so the means before and after the treatment are same this result suggests that the drug treatment does not have a significant effect