Question

For a comparison of two study guides for a mathematics course, 12 student volunteers were found. They were randomly assigned, 6 to study guide A, and 6 to study guide B. Following a two-day period of independent study, the students were examined on the material. The students received the following scores (out of 100):

Study Guide A: 90 95 91 80 94 91
Study Guide B: 66 72 81 62 80 67

Use a permutation test to test the null hypothesis that the distributions of scores are the same for each study guide, against the two-sided alternative that the distributions are different. Test statistic: 18.8333

How many arrangements of the data would lead to an absolute value of the computed test statistic as great or greater than the absolute value of the test statistic you calculated in the previous question? Note that you don't have to list all possible arrangements in order to answer this.

Answer 1

as for A there are 3 options for bottom value; 80,80 and 81 ; cause 2 values are same therefore 2 options are there and as values in guide A and B are interchangeable

therefore arrangements of the data would lead to an absolute value of the computed test statistic as great or greater than the absolute value of the test statistic you calculated in the previous question

=2*2 =4