Sleep Medicine for Shift Workers

Shift workers, who work during the night and must sleep during the day, often become sleepy when working and have trouble sleeping during the day.

In a study done at Harvard Medical School, 209 shift workers were randomly divided into two groups; one group received a new sleep medicine (modafinil, or Provigil), and the other group received a placebo.

During the study, 54% of the workers taking the placebo and 29% of those taking the medicine reported accidents or near accidents commuting to and from work. Assume that 104 of the people were assigned the medicine and 105 were assigned the placebo.

(Source: Czeisler et al., Modafinil for excessive sleepiness associated with shift-work sleep disorder, New England Journal of Medicine, vol. 353: 476-486, August 4, 2005)

a. State the null and alternative hypothesis. Is the alternative hypothesis one-sided or two-sided? Explain your choice.

b. Perform a statistical test to determine whether the difference in proportions is significant at the 0.05 level.