The European Journal of Engineering Education (Vol. 38, 2013) published a study of the feasibility of adding a general engineering program to a university’s specialized engineering programs (e.g., civil, mechanical, electrical engineering). A pre liminary study found that about half (50%) of engineering students responded favorably to a general engineering program. Let Y represent the number of students in a sample of 10 who favor a general engineering program and let p represent the true proportion of all students who favor a general engineering program. Suppose you want to test H_o: p = .5 against H_a: p ≠ .5. One possible procedure is to reject H_o if  Y ≤ 1or Y ≥ 8.
a. Find α for this test.
b. Find β if p = .4. What is the power of the test?
c. Find β if p = .8. What is the power of the test?