Aclinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 minutes. after treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and a standard deviation of 42.3 minutes (based on data from cognitive behavioral therapy vs zopiclone for treatment of chronic primary insomnia in older adults," by silverstein et al., journal of the american medical association, vol. 295, no. 24). assume that the 16 sample values appear to be from a a normally distributed population and construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments. what does the result suggest about the mean wake time of 102.8 minutes before the treatment

A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is,

From the standard normal table, the z-critical value at 98% confidence is 2.33

98%C.I. = µ ± z * σ /  sqrt of n = 98.90 ± 2.33 * 42.30 / sqrt of 16  = 98.90 ± 24.64 = 74.26 to 125.54

A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

The result does not suggest about the mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.

To calculate for the confidence interval, we use the formula:

CI = x ± t * s / sqrt(n)

where CI is the confidence interval, x is the mean value, t is the t score which is taken from the tables at 98% confidence interval, s is standard deviation, and n is number of samples

From the tables at 98% and DOF = n – 1 = 15

t = 2.131

CI = 98.9 ± 2.131 * 42.3 / sqrt(16)

CI = 98.9 ± 22.5

CI = 76.4, 121.4

76.4 min ≤ wake time ≤ 121.4 min

So the wake time values range from 76.4 min to 121.4 min. Since the original mean wake time is 102.8 min, so it still inside the interval and hence the drug was ineffective.