The flu vaccine protects individuals from being infected with the Influenza virus. Although it is not 100% effective, the duration of illness in vaccinated individuals is thought to be shorter than that of unvaccinated individuals. To test this theory, the health department surveyed a total of 1000 individuals who became infected with Influenza (500 vaccinated, 500 unvaccinated). The participants reported the number of days they were symptomatic for.

What are the competing hypothesis statements for this test?