Are the outcomes of hospital care different on weekends than weekdays?

In a random sample of 500 patients who experienced severe medical complications after admission to acute care wards in three U.S. states from 1999 and 2001, 119 had been admitted on a weekend and 381 had been admitted on a weekday. This compares with a large population of people at risk for such complications in which 14.8% are admitted on weekends and 85.2% are admitted on weekdays (Bendavid et al. 2007).

a. In the 500 sampled patients with severe complications, what fraction had been admitted on weekends? Is this higher or lower than the fraction of all at-risk patients admitted on weekends?

b. Name two statistical methods that could be used to test whether the probability of severe complications in at-risk patients admitted to hospitals differs between weekend and weekday. State the advantages and disadvantages of both.

c. State the null and alternative hypotheses for such a test.

d. Test the hypotheses. State your conclusions clearly.