A helmet company is testing whether football helmets containing special force padding were effective in reducing the number of concussions in NCAA football players. The following table summarizes the data comparing the number of concussions during the 2021 season according to the new helmet vs. traditional helmets.

Helmet Concussion No Concussion

New 18 32

Traditional 27 23

a. Calculate BY HAND the appropriate test statistic to determine whether there is a statistically significant association between helmet type and concussions (show your work)

b. Which type of helmet appears better for preventing concussions ?

c. Of those using traditional helmets, what proportion received a concussion?

d. What are the odds of sustaining a concussion using a new helmet relative to using a traditional helmet?