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

97.9

min and a standard deviation of

21.8

min. Assume that the

13

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.

minless than<muμless than<

min

​(Round to one decimal place as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 97.9 min.

sample standard deviation = s = 21.8 min.

sample size = n = 13

Degrees of freedom = df = n - 1 = 13 - 1 = 12

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,12 = 2.179

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

= 2.179 * (21.8 / 13)

Margin of error = E = 13.2

The 95% confidence interval estimate of the population mean is,

- E < < + E

97.9 - 13.2 < < 97.9 + 13.2

( 84.7 min. < < 111.1 min. )

The confidence interval include the mean wake time of 103.0 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