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