According to work done by Nick Wilson of Otago University Wellington, the proportion of individuals who cover their mouth when sneezing is 0.733. As part of a school project, Mary decides to confirm the work of Professor Wilson by observing 100 randomly selected individuals sneeze and finds that 78 covered their mouth when sneezing.

(a) What are the null and alternative hypotheses for Mary’s project?

(b) Verify the requirements that allow use of the normal model to test the hypothesis are satisfied.