The overall pass rate for law school graduates taking the Maryland bar exam has

Question

The overall pass rate for law school graduates taking the Maryland bar exam has been reported as 76%. Assume that a certain Maryland law school has had 400 of its most recent graduates take the Maryland bar exam, but only 60% passed. When asked about these results, the dean of this university's law school claims his graduates are just as good as others who have taken the Maryland bar exam, and the low pass rate for the recent graduates was just "one of those statistical fluctuations that happen all the time." If this university's overall pass rate for the Maryland bar exam were really 76%, what would be the probability of a simple random sample of 400 having a pass rate of 60% or less? Based on this probability, comment on the dean's explanation.

Explanation / Answer

n=400

p=0.76

Standard error = sqrt( p*(1-p)/n))

=sqrt(0.76*0.24/400)=0.0214

Z value for 0.6, z=P( 0.6-0.76)/0.0214 = -7.49

P( p0.6) = P( z < -7.49) =0.0000

This probability is < 0.05, the event is unusual.

The Dean’s explanation is not correct.

There is no statistical fluctuation, the data shows that this law school is below the 76%

Pass rate.

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