A test preparation agency offers classes to people who are planning to take the

Question

A test preparation agency offers classes to people who are planning to take the Law
School Admissions Test. Of the agency's clients, 65% are undergraduate students,
25% are graduate students, and 1 0% are people not currently attending schooL The
agency claims that 80% of its clients improve their scores by taking its preparatory
classes. It bases this claim on sample tests which each client takes before and after
completion of its classes.
a. In a recent survey of students who had enrolled in the agency's course, 80% of
the undergraduates and 50% of the graduates said that their scores improved by
taking the course. If these numbers are accurate, what does this suggest about the
agency's claim? Explain.
b. In a different survey of students who had enrolled i n the course, 95% of the
undergrads and 75% of the grads said that their scores improved. What does this
suggest about the agency's claim? Explain.
c. In yet another survey of students who had enrolled i n the course, 70% of the
undergrads and 50% of the grads said that their scores improved by taking the
course. Based on these numbers, what is the highest success rate that the agency
can possibly claim? What is the smallest possible value for the probability that a
client's score improved?

Explanation / Answer

a)80% * 65%= 52% and 50%* 25%=12.5%

52% +12.5%= 64.5%-proportion of students who improved based on survey. The agency's claim is overestimated.

b)95%*65%=61.75%

75%*25%=18.75%

total =80.5% The agency's claim is valid

c)70%*65%=45.5%

50%*25%=12.5%

total=58%

Based on these numbers, the highest success rate that the agency
can possibly claim is

80.5% and the smallest possible value for the probability that a

client's score improve is 58%

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