The authors of a paper titled "age and violent content labels make video games forbidden fruits for youth" carried out an experiment to determine if restrictive labels on video games actually increased the attractiveness of the game for young game players.

participants read a description of a new video game and were asked how much they wanted to play the game. the description also included an age rating. some participants read the description with an age restrictive label of 7+, indicating that the game was not appropriate for children under the age of 7. others read the same description, but with an age restrictive label of 12+, 16+, or 18+.

the summary data shown below are the ratings of 12- to 13-year-old boys for how much they wanted to play the game on a scale of 1 to 10. you can assume that boys were assigned at random to one of the four age label treatments (7+, 12+, 16+, 18+) and that ratings were normally distributed.

group sample size sample mean sample std dev
7+ label 10 5.3 1.96
12+ label 10 7 1.55
16+ label 10 8.5 1.59
18+ label 10 8.2 1.59

(a) what is the sum of all observations in the data set? t =