Question

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

1414

subjects had a mean wake time of

100.0100.0

min. After​ treatment, the

1414

subjects had a mean wake time of

78.578.5

min and a standard deviation of

22.722.7

min. Assume that the

1414

sample values appear to be from a normally distributed population and construct a

9595​%

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

100.0100.0

min before the​ treatment? Does the drug appear to be​ effective?

Construct the

9595​%

confidence interval estimate of the mean wake time for a population with the treatment.

minless than<muμless than<nothing

min

Answer 1

Answer:

Given,

degree of freedom = n - 1 = 14 - 1 = 13

alpha = 0.05

t(alpha/2 , df) = t(0.05/2 , 13) = 2.160369 = 2.16

95% CI = xbar +/- t*s/sqrt(n)

substitute values

= 78.5 +/- 2.16*22.7/sqrt(14)

= 78.5 +/- 13.1044

= (65.4 , 91.6)

65.4 < u < 91.6

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