A school principal is interested in a new method for teaching eighth grade social studies, which he believes will increase the amount of material learned. To test this method, the principal conducts the following experiment. The eighth grade students in the school district are grouped into pairs based on matching their IQ and past grades. Twenty matched pairs are randomly selected for the experiment. One member of each pair is randomly assigned to a group that is taught using the new method, and the other member of each pair to a group receives standard instruction. At the end of the course all students take a common final exam. The following are the students scores on the exam:
PAIR # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
New Method 95 75 73 85 86 86 93 88 75 84 72 84 75 87 94 82 70 84 72 83
Standard Instruction 83 68 80 82 84 78 85 82 84 68 81 91 72 81 83 87 65 76 63 80
Compute the difference in each pair of scores. Then compute the sign test statistics by using a cut-point of 0 ("zero"). A) what value did you calculate for the "test statistic" of the sign test? B) What is the alternative hypothesis? C) What is the null hypothesis? D) Why does a cut-point of zero (0) make sense for this data set? E) Using α = 0.051tail , can the principal conclude that the new method improves student learning? F) What is the type of error you might be making as result of your conclusion in part c? G) To what population does your conclusion apply?