Question

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the​ drug, 14 subjects had a mean wake time of 92.9 min and a standard deviation of 42.9 min. Assume that the 14 sample values appear to be from a normally distributed population and construct a 98​% confidence interval estimate of the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is​ effective?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 92.9

sample standard deviation = s = 42.9

sample size = n = 14

Degrees of freedom = df = n - 1 = 14 - 1 = 13

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t0.01,13 = 2.650

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

= 2.650 * (42.9 / 14)

Margin of error = E = 30.4

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

- E < < + E

92.9 - 30.4 < < 92.9 + 30.4

( 62.5 min. < < 123.3 min.)

Yes, the confidence interval indicates that the treatment is effective because the interval does not contain 0 minutes.