A university is measuring the proportion of successful applicants from the pool of total applicants for their business faculty. From one report of an entire open day, a representative sample of size 335 is taken from the population of applicants to a university’s MBA program.

It shows 190 applicants in the sample applied to study business at the undergraduate level.

a. Testing at a 5% level of significance, is there strong statistical evidence that more than 60% of all the applicants in the population studied business at the undergraduate level?

b. Determine the power of the test for part

a, if in fact the true proportion is 65%.