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+ label676548612412+ label878579584716+ label798675896718+ label109697689108

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?₄be 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.)

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 ofa 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+Iabel6765486124 12+Iabel8785795847 16+Iabel7986758957 18+Iabel109697689108 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 signicance level of 0.05. (Let \"1' 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 four different age label treatments.) State the appropriate null and alternative hypotheses. Ho:l'1="2=l'3=\"4 Ha : all four of the ui's are different H0 : at least two of the four yi's are different Ha:\"1=\"2=\"3=l'4 Ho=l'1=\"2=l'3=\"4 Ha : at least three of the four ui's are different H0 : all four of the ui's are different H531=z=3=4 oHo=M1=u2=M3=u4 Ha : at least two of the four ui's are different J 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 = 6.22 x P-value = .002 X