Scores on a certain IQ test are known to have a mean of 100 . A random sample of 60 students attend a series of coaching classes before taking the test. Let \(\mu\) be the population mean IQ score that would occur if every student took the coaching classes. The classes are successful if \(\mu>100\). A test is made of the hypotheses \(H_{0}: \mu \leq 100\) versus \(H_{1}: \mu>100\).

a. Assume that the classes are successful, but the conclusion is reached that the classes might not be successful. Which type of error is this?

b. Assume that the classes are not successful. Is it possible to make a type I error? Explain.

c. Assume that the classes are not successful. Is it possible to make a type II error? Explain.