To help students gauge their understanding of basic concepts, short online quizzes with immediate feedback were administered in an introductory statistics (STAT) and an unrelated computer science (CS) course in the first few weeks of the semester. For those students who realized they knew less than they thought after taking the quizzes, did this change their study habits? All 5 students in the STAT course said it did, whereas 6 of the 12 students in the CS course said it did. Is there evidence that students in the STAT course had a larger probability of changing their habits?
a. Write these results as a 2 × 2 contingency table.
b. The sampling distribution (derived from all possible 6188 permutations) for the possible counts in the first cell of the contingency table is

Find the proportion of tables that have a cell count as large or larger than the one observed.
c. Find the permutation P-value and write a conclusion for the hypothesis when using a 5% significance level.

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4 4 Total cell count: 5 #perms: 6 165 1100 2475 1980 462 6188