A classic psychological test involves adding a set of numbers (e.g., 1,000 + 40 + 1,000 + 30 + 1,000 + 20 + 1,000 + 10) to evaluate cognitive behavior. In a study published in Advances in Cognitive Psychology (Jan. 2013), undergraduate students were all given the serial addition task, with the numbers presented on a computer screen. One group (n1 = 60 students) saw each of the numbers for 2 seconds on the screen. A second group (n2 = 60 students) saw all the numbers on the screen at the same time, with the number 1,000 presented in bright red. The correct answer, of course, is 4,100. In the first group, 17 answered correctly; in the second group, 12 answered correctly.
a. Compute the proportion of students in Group 1 that answered correctly.
b. Compute the proportion of students in Group 2 that answered correctly.
c. Why is a statistical test of hypothesis (or confidence interval) required to compare the sample proportions, parts a and b?
d. Conduct a test (at a = .01) to compare the proportions. What inference can the researchers make regarding the two serial addition tasks?