Question

Please answer clearly and precisely as possible.

2) Dan Ariely and colleagues have conducted some extremely interesting studies on cheating (see, for example Mazar, Amir, & Ariely, 2008). To provide an opportunity for cheating, participants are given a packet of problems and told they will be paid $0.50 for each correct answer. The experiment is setup, however, so that the participant doesn't have to turn in their work, they simply have to state how many problems they solved to get paid. This provides a prime opportunity to cheat to earn extra money. In previous tests where the problems are properly scored, so no cheating, Ariely and colleagues found that scores are normally distributed: 3.3, 1.0. Here is a list of scores for participants who knew that their work would not be checked. Which of these would you suspect of cheating? Why? a. Participant 1: X-.4 b. Participant 2: X- 6 . Participant 3: X7 d. Participant 4: X-0 9 3) Continuing from the previous question, would it be possible to create a hard and fast rule to identify cheaters based solely on the scores they report? For example, could you determine that anyone with z > 3 must have cheated because, without cheating, this is expected to be a rare level of performance? With this standard, would it be possible to falsely accuse a participant of cheating? If you raise the standard (say z > 4) to reduce the risk of making a false accusation, what other problem does this produce? 0

Answer 1

-3.3, sd- 1

P( < 4) p( = p(z < .7) = 0.75804 sd

P 6) sd = p(z < 2.7) = 0.99653

P s 7) X-μ 7-3.3 4 = p(s < 3.7) 0.99989

P 0) p( sd = p(2 <-3.3) 0.00048

the participant with score=4 is the only one not cheating,reat of them are cheating because their score is outside the value of 95% confidence interval.