A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects.

Question

After treatment with the​ drug, 30 subjects had a mean wake time of 91.5 min and a standard deviation of 40.5

min. Assume that the 30 sample values appear to be from a normally distributed population and construct a

90​% 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?

A)Find the confidence interval estimate

B)Does the result indicate whether the treatment is​ effective?

a) Yes, the confidence interval indicates that the treatment is effective because the interval contains 0 minutes.

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

c)​No, the confidence interval does not indicate whether the treatment is effective.

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

e)Yes, the confidence interval indicates that the treatment is effective because the interval does not contain 91.5 minutes.

f)Yes, the confidence interval indicates that the treatment is not effective because the interval contains 0 minutes

g)​Yes, the confidence interval indicates that the treatment is not effective because the interval does not contain 91.5 minutes.

Answer 1

CI = mean +/- z-critical * standard deviation/square root(sample size)

= 91.5 +/- 1.645 * 40.5/sqrt(30)

= 79.34, 103.66

The confidence interval does not indicate that the treatment is effective (c).