A group of high-risk high school students was identified in the **winter of 1998-1999** who had 3+ previous episodes of influenza before December 21, 1998. There were 20 students in this group, each followed for 90 days, of whom 8 developed influenza. Test the hypothesis that the high risk students had a higher incidence rate of influenza than the average high school student during the **winter of 1998-1999**. Write out all 4 steps of the hypothesis test including a one-tailed $p$-value