The college of business at a state university has a computer literacy requirement for all graduates. Students must show proficiency with a computer spreadsheet software package and with a word-processing software package. 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 microcomputer 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 this. 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 0.05, what conclusions should the administrators make regarding the difficulty of the test?
b. Describe a Type II error in the context of this problem.