Reference no: EM132746772

Suppose that a set of examination questions are sent to a class of 40 students, the responses to which are due a couple of weeks thereafter. Among the submitted responses, there is a subset of more than 20 submissions that exhibit a striking similarity of content and verbal formulation, a similarity all the more remarkable given the fact that most of the answers are incorrect, some incorrect in a quite bizarre way . Some flavor of two of the most egregious of these answers are captured by the following illustration, carefully crafted to give an indication of the various dimensions along which the responses go radically wrong: Question: "Pick a prime number between 100 and 1,000, and, using the method discussed in class, calculate its square root to three decimal places". In response, 20 students select the number 64, and all 20 give the number 9.32184 as its square root.

Approaching this puzzle in accordance with the mode of analysis embodied in Bayes' Theorem, how would one go about evaluating the relative probabilities of hypotheses such as H1)Each student selected the number and derived this answer independently of the others; H2)The students worked together to gain an understanding of the indicated method of extracting square roots, and then each proceeded independently to select a number and work out its square root; H3)The students all utilized a uniquely easily accessible source to understand the method for the extraction of roots, but then fell into the same natural mistake in calculating the square root.

Question 1: Discuss whether any of these hypotheses provide plausible explanations of these responses. Are there other a priori plausible hypotheses that might account for this response? For each of the hypotheses H1, H2, and H3, construct a (less extreme) variant of this illustration that makes that hypothesis plausible.