Tovan is interested in studying whether the brightness of a room affects scores on a math test - specifically, he wants to see whether scores on a math test differ when completed in a darkly lit classroom vs a brightly lit classroom. He wants to collect 30 observations in each condition. (10 pts)

a)Describe how Tovan could design his study if he wanted to use a between-subjects design. Your design should include (i) how many participants should participate in the study, (ii) what statistical test should be used to analyze the data, and (iii) how to best design the study to address any possible limitations.

b) Describe how Tovan could design his study if he wanted to use a within-subjects design. Your design should include (i) how many participants should participate in the study, (ii) what statistical test should be used to analyze the data, and (iii) how to best design the study to address any possible limitations.

c) If Tovan knows the math scores when completed in a brightly lit classroom compared to a darkly lit classroom, can he confidently conclude that math scores will be somewhere in the middle when completed in a medium-brightness room? Describe why or why not. If not, make sure to describe examples of why this might not be accurate.

d) How could Tovan design a future study to better compare math scores in medium- brightness room compare to math scores in a darkly lit and a brightly lit classroom? Your answer does not need to include sample sizes, but should include the type of statistical test used to analyze the data.