The following questions are based on Paired-Data

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? Or is it coincidental, that is, do students who chose to play instruments tend to have higher math scores than those who do not? 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. So 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 where their mouths are. They have each wagered $50, with the winner keeping the sum. Your job is to decide who wins. Here is the data: Group Data 1. Piano 1. Piano 1. Piano 1. Piano 1. Piano 2. Puzzle 2. Puzzle 2. Puzzle 2. Puzzle 2. Puzzle 3 4 5 6 7 5 6 7 8 9 Use the same data as the Piano vs Puzzle problem. What if the data was collected in a within-subject design (The same five people experience both the Piano and Puzzle conditions at a different time)? Question 7 1 pts Use the same data as the Piano vs Puzzle problem but the data was collected in a within-subject design. Calculate the SSE for the Null model: Question 8 1 pts Use the same data as the Piano vs Puzzle problem but the data was collected in a within-subject design. Calculate the SSE for the Effects model: Question 9 1 pts Use the same data as the Piano vs Puzzle problem but the data was collected in a within-subject design. Calculate the R-squared for the effects model: Question 10 2 pts In the Piano vs Puzzle problem, which designs yielded a higher R-squared? Paired Data (Within) OTwo-Groups (Between)