A clinical trial was conducted to test the effectiveness of the drug Zopiclone f

Question

A clinical 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 98.9 min and a standard deviation of 42.3 min. Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with Zopiclone, subjects have a mean wake time of less than 102.8 min (the sample's mean wake time before treatment). Does Zopliclone appear to be effective?

(Based on data from "cognitive Behavioral Therapy vs Zopiclone for Treatment of Chrinic Primary Insomnia in Older Adults," by Siversten, etal., Journal of the American Medical Association, Vol. 295, No. 24.)

Explanation / Answer

here null hypothesis: mean =102.8

alternate hypothesis: mean<102.8

std error of mean =std deviaiton/(n)1/2 =10.575

hence test stat t=(X-mean)/std error =(98.9-102.8)/10.575 =-0.3688

for above test stat p value =0.3587

as p value is very high we can not conclude that  subjects have a mean wake time of less than 102.8 min

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