The authors of a paper on perceptions of video games 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 following data for 12- to 13-year-old boys 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 (7+, 12+, 16+, and 18+). Data shown are the boys' ratings of how much they wanted to play the game on a scale of 1 to 10. 7+ label 6765586124 12+ label 87 10 5795847 16+ label 7986758967 18+ label 10 96 97 68 9 10 8 Do the data provide convincing evidence that the means of the ratings associated with the game descriptions 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 0.05. (Let H2 H3 and 4 be the true mean ratings of how much 12- to 13-year-old boys want to play the game on a scale of 1 to 10 for the four different age label treatments.) State the appropriate null and alternative hypotheses. H: all four of the 's are different H: at least three of the four 's are different O Ho: at least two of the four 's are different O Ho: all four of the μ's are different HHH2 H3 H4 H, at least two of the four 's are different Find the test statistic. (Round your answer to two decimal places.) F= Use technology to find the P-value. (Round your answer to four decimal places.) P-value= State the conclusion in the problem context. ○ we reject Ho. 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. We reject Ho. The data do not 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. We fail to reject Ho. 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. We fail to reject Ho. The data do not 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.