To assess whether students are computer literate, a test is given at the end of each semester. The test is designed so that at least 70% of all students who have taken a special micro-computer course will pass. The college does not wish to declare that fewer than 70% of the students pass the test unless there is strong sample evidence to indicate that. Suppose that, in a random sample of 100 students who have recently finished the microcomputer course, 63 pass the proficiency test.

(a) Using a significance level of 0.015, what conclusions should the administrators make regarding the difficulty of the test?

(b) Find a 97% confidence interval for the true proportion of the students passed.