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 gameplayers. 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 descriptionwith 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 canassume 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 scaleof 1 to 10.7+ label12+ label7 68 716+ label 7 918+ label 10 96 5 5 8 6 110 58676 7H₂ M₁ = H₂ = μ3 = μ4H: all four of the μ's are different94State the appropriate null and alternative hypotheses.Ho: all four of the μ's are differentH₂ M₁ = H₂ = μ3 = μ₁4:O Ho : at least two of the four μ's are differentH₂ = μ₁ = μ₂ = μ3 = μ₁4Ho: M₁ = μ₂ = μ3 = μ²4H: at least two of the four μ's are different5 88 9O H₁ H₁ = μ₂ = μ3 = μ₁H₂ : at least three of the four μ's are different2 448 7 6 8 9 10 8Do 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 theappropriate hypotheses using a significance level of 0.05. (Let M₁, M₂, M3, 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 fourdifferent age label treatments.)677Find 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.O 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.O 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 ratinglabels.O 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.O 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.

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 12+ label 7 6 6 5 5 8 6 12 4 8 7 10 5 7 9 16+ label 7 9 8 18+ label 10 6 7 4 96 8 7 6 State the appropriate null and alternative hypotheses. O Ho: all four of the μ's are different H₂H₁ = H₂ = H3 = 14 O H₁ H₁ H₂ = H3 = 14 H₂: all four of the μ's are different O Ho: at least two of the four μ's are different H₂H₂ = H₂ = H3 = μ4 H₁ H₂ = H₂ = μ3 = 14 H: at least two of the four μ's are different 5 O H₁ H₂ = H₂ = 13 = 14 H.: at least three of the four μ's are different 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 H₁ 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.) 8 9 4 7 6 7 8 9 10 8 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. O 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. Owe 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. O 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. Owe 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.