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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 6 6 5 8 6 2 12+ label 8 16+ label 9 8 6 18+ label 10 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 #1, #2, #3, 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. O Ho : H1 = H2 = M3 = H4 H : all four of the u,'s are different O Ho : all four of the u.'s are different Ha : H1 = H2 = H3 = H4 O Ho : H1 = H2 = H3 = H4 H : at least two of the four u,'s are different O HO : H 1 = 42 = Hy = H4 He : at least three of the four u's are different O Ho : at least two of the four u.'s are different Ha : H1 = H2 = H3 = H4 Find the test statistic and P-value. (Use technology. Round your test statistic to two decimal places and your P-value to three decimal places.) F = 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 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. 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.Tutorial Exercise 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 5 5 5 4 4 7 5 w 12+ label 7 6 9 4 6 8 4 7 3 5 16+ label 6 8 7 5 3 8 5 6 18+ label 8 5 8 5 9 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 My, u2, u;, and u 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.) Click here to begin!The authors of the paper "Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth"t 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 paper gave data for 12- to 13-year-old girls. Data consistent with summary values in the paper are shown below. 7+ label 12+ label 16+ label 18+ label 6 4 8 5 4 6 6 5 8 6 5 6 6 7 5 3 10 7 6 5 10 4 4 3 6 10 5 8 6 6 10 5 8 8 5 9 5 7 Do the data provide convincing evidence that the mean rating associated with the game description for 12- to 13-year-old girls is not the same for all four age restrictive rating labels? Test the appropriate hypotheses using a = 0.05. Calculate the test statistic. (Round your answer to two decimal places.) F = What can be said about the P-value for this test? O P-value > 0.100 O 0.050 0.100 0 0.050 0.100 O 0.050
