15.5 The authors of the paper “Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth”

(Pediatrics [2009]: 870–876) 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 71, 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 121, 161, or 181.
The data below for 12- to 13-year-old boys are fictitious, but are consistent with summary statistics given in the paper. (The sample sizes in the actual experiment were larger.) For purposes of this exercise, you can assume that the boys were assigned at random to one of the four age label treatments (71, 121, 161, and 181). Data shown are the boys’
ratings of how much they wanted to play the game on a scale of 1 to 10.
Do the data provide convincing evidence that the mean rating associated with the game description by 12- to 13-year-old boys is not the same for all four restrictive rating labels? Test the appropriate hypotheses using a significance level of .05. (Hint: See Example 15.4.)
71 label 121 label 161 label 181 label 6 8 7 10 6 7 9 9 6 8 8 6 5 5 6 8 4 7 7 7 8 9 4 6 6 5 8 8 1 8 9 9 2 4 6 10 4 7 7 8