A teacher gives a test to her classes before and after showing them a particular educational video. A random sample of 18 of these students is selected. It was found that 12 of these students had a higher post-video test score, 4 of them had a lower post-video test score, and 2 students had equal pre- and postvideo test scores. The sign test at the 0.01 significance level will be used to test the claim that the video affects students' test scores. (a) What is the value of the test statistic used in this sign test?

Step 1 ：A teacher gives a test to her classes before and after showing them a particular educational video. A random sample of 18 of these students is selected. It was found that 12 of these students had a higher post-video test score, 4 of them had a lower post-video test score, and 2 students had equal pre- and postvideo test scores. The sign test at the 0.01 significance level will be used to test the claim that the video affects students' test scores.

Step 2 ：The sign test is a non-parametric test used to test the hypothesis about the median of a population. In this case, we are testing the claim that the video affects students' test scores.

Step 3 ：The test statistic for the sign test is calculated as the number of positive differences (i.e., the number of students who had a higher post-video test score). However, in the sign test, we do not consider the observations where the pre- and post-video test scores are equal. So, we will only consider the 16 students who had either a higher or lower post-video test score.

Step 4 ：Calculate the number of positive differences, negative differences, and total differences. The positive differences are 12, the negative differences are 4, and the total differences are 16.

Step 5 ：The test statistic is equal to the number of positive differences, which is 12.

Step 6 ：\(\boxed{12}\) is the value of the test statistic used in this sign test.