The test preparation agency presents classes to people who are preparing to take Law School Admissions Test. Of agency's clients, 25% are graduate students, 65% are undergraduate students, and 10% are people not presently attending schooL Agency claims that 80% of clients improve the scores by taking preparatory classes. It bases this claim on sample tests that every client takes before and after completion of the classes.
a. In the recent survey of students who had enrolled in agency's course, 80% of undergraduates and 50% of graduates said that the scores improved by taking course. If the numbers are accurate, what this suggests about agency's claim? Describe.
b. In the different survey of students who had enrolled in course, 95% of undergrads and 75% of grads said that scores improved. What this suggests about agency's claim? Describe.
c. In yet another survey of students who had enrolled in course, 70% of undergrads and 50% of grads said that their scores enhanced by taking course. Based on the numbers, find highest success rate that agency can possibly claim? Determine smallest possible value for probability that client's score enhanced?