Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 25.4 with a standard deviation of 4.9 , while the 200 students in group 2 had a mean score of 15.2 with a standard deviation of 3 .

(a) Determine the \(90 \%\) confidence interval for the difference in scores, \(\mu_{1}-\mu_{2}\). Interpret the interval.

(b) What does this say about priming?