Question

A clinical trial was conducted to test the effectiveness of a drug for treatment insomnia in older subjects. Before treatment, 13 subjects had a mean wake time of 102.0 min. After treatment, the 13 subjects had a mean wake time of 92.4 min and a standard deviation of 22.1 min. Assume that 13 samples value 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 102.0 min before the treatment? Does the drug appear to be effective?

-----min < u <----- min. What does the result suggest about the mean wake time of 102.0 min before the treatment? Does the drug appear to be effective?

The confidence interval -------------------the mean wake time of 102.0 min before the treatment, so the means before and after the treatment --------------------this result suggests that the drug treatment ------------------a significant effect.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 92.4 min.

sample standard deviation = s = 22.1 min.

sample size = n = 13

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

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

t/2,df = t_0.005,12 = 3.055

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

= 3.055 * ( 22.1 / 13)

Margin of error = E = 18.7

The 99% confidence interval estimate of the population mean is,

- E < < + E

92.4 - 18.7 < < 92.4 + 18.7

( 73.7 min. < < 111.1 min.)

The confidence interval include the mean wake time of 102.0 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