Who can catch a liar? Not everyone you might think, according to a well-known study which investigated the ability of police, judges, secret service agents, and university students to distinguish between videos of liars and truth-tellers. By random guesswork each participant would be expected to classify 50%

of the videos correctly. The university students did only a little better than guesswork, with an average of 53% correct classifications, while the professionals weren’t much better at around 56% correct. The secret service agents were far and away the best, and even they only scored 64%.
What’s the moral of this story? Try not to get arrested for a crime you didn’t commit.

a. The police professionals in the study attempted a total of 1260 classifications, and got 703 correct. Construct an approximate 95% confidence interval for the probability p that a police professional can correctly distinguish truthtellers from liars in the context of this study.

b. The university students in the study attempted a total of 390 classifications, and got 206 correct. Construct an approximate 95% confidence interval for the probability q that university students can make correct classifications.

c. Compare the two intervals for police and university students. Do you think this constitutes evidence that the police are better than the students?

d. Why is the interval for the police professionals so much narrower than that for the students?