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? 12
(b) What is the critical value in this sign test? 14
(c) What is the correct conclusion of this sign test?
There is sufficient evidence to warrant rejection of the claim that the video affects students' test scores.
There is not sufficient evidence to support the claim that the video affects students' test scores.
There is sufficient evidence to support the claim that the video affects students' test scores.
There is not sufficient evidence to warrant rejection of the claim that the video affects students' test scores.

Step 1 ：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 2 ：The test statistic in a sign test is the number of successes, which in this case is the number of students who had a higher post-video test score. The test statistic value is \(12\).

Step 3 ：The critical value is a threshold that the test statistic must exceed in order for us to reject the null hypothesis. In this case, the critical value is \(14\).

Step 4 ：To determine the conclusion of the sign test, we compare the test statistic to the critical value.

Step 5 ：If the test statistic is greater than or equal to the critical value, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

Step 6 ：If the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim.

Step 7 ：The test statistic (\(12\)) is less than the critical value (\(14\)), so we fail to reject the null hypothesis.

Step 8 ：This means that there is not sufficient evidence to support the claim that the video affects students' test scores.

Step 9 ：\(\boxed{\text{Final Answer: There is not sufficient evidence to support the claim that the video affects students' test scores.}}\)