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 102.8 min....

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 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a sample standard deviation of 42.3 min (based on data from “Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,” by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). 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.

1. Using the most relevant test statistic, find the critical value - what is it?
2.  Sketch a normal distribution curve, plot the critical value, and highlight the critical or rejection region.
3.  Calculate the test stastic based on sample data.  Plot the test statistic on your graph.
4.  State a conclusion about the null hypothesis (reject H0 or fail to reject H0).  Does zopiclone appear to be effective - why or why not?