According to a college guide, selective means that the average SAT score of incoming freshmen is 600, with a standard deviation of 50. A high school guidance counselor suspects that many colleges rated by the guide as selective do not meet the guide's standard. He randomly selects 30 colleges rated by the guide as selective. He then asks the admissions officer at each of the 30 colleges for the average SAT scores of the college's entering freshmen. The average SAT score of entering freshmen at the 30 schools turns out to be 562.
a. State the null hypothesis.
b. Calculate the normal deviate Z test.
c. What is the probability that the average SAT score for these 30 colleges would be so far below the stated 600 average if the guide's claim is really true?