Did you know that higher mathematics performance in middle school is correlated with playing a musical instrument? Is this relationship causal, that is, does it playing an instrument in itself lead to mental changes that lead to better math abilities? Dr is it coincidental, that is, do students who chose to play instruments tend to have higher math scores than those who do not?I Pin-Chun and Paulina have made a bet. Pin'Chun thinks that the relationship is causal playing an instrument causes greater math scores. Paulina thinks that performing spatial activities, such as doing jigsaw puzzles should be best for improving math. 5o Pin'Chun and Paulina run an experiment. Middle-schoolers are randomly assigned to either the piano or puzzle group, with the former taking piano lessons, and the latter solving jigsaw puzzles. Then, afterwards, a math exam is given. Alex is more skeptical about it; he doesn't think any of these activities affect math scores. So, the scores shouldn't differ among the groups. Pin-Chun, Paulina, and Alex have put their money 1where their mouths are. They have each wagered $50, with the winner keeping the sum. Yourjob is to decide who wins. Here is the data: Group Data . Piano . Piano . Piano . Piano . Piano . Puzzle . Puzzle . Puzzle . Puzzle . Puzzle MHMMMlIhIIIIilI tom-ammuqmcnmm Match each model with their correspondingr notation if we know that yij is the j' participant in the i1H1 group [i=1 denote the Piano group; i=2 denote the Puzzle group]. 1. Null model 2. Effects Model 1 ' [ Choose ] v ' 2 ' [ Choose ] V i Continue to the Piano vs Puzzle problem. Whose position does the null model and the effects model correspond to, respectively? Pin-Chun [ Choose ] Paulina [ Choose ] v Alex [ Choose ]Continue to the Piano v5 Puzzle problem. Calculate the SSE for the Hull model: Question 5 Continue to the Piano v5 Puzzle problem. Calculate the 55E for the Effects. model: Question 6 Continue to the Piano 1:5 Puzzle problem. Based on SSE, who 1won the bet? 0 PinvChun {j Paulina 0 Alex