The authors of a paper on perceptions of video games carried out an experiment to determine if restrictive labels on video games actually increasedthe attractiveness of the game for young game players. Participants read a description of a new video game and were asked how much they wantedto play the game. The description also included an age rating. Some participants read the description with an age-restrictive label of 7+, indicatingthat 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 actualexperiment were larger.) For purposes of this exercise, you can assume that the boys were assigned at random to one of the four age labeltreatments (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 6 765 512+ label 816+ label 78 50⁰76 718+ label 10 9 6 8 7о но : H1 = M2 = μз =H4836129Ha : all four of the μ's are different5сState the appropriate null and alternative hypotheses.O Ho: all four of the µ's are differentНа: М1=M2=μз=Нано: М1 = M2 = μз =H4Ha at least two of the four μ's are different6 8оно : H1 = H2=μз = наH₂ : at least three of the four μ's are different5Ho : at least two of the four μ's are differentНа: М1 =M2 = μ3=1488 994Do 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 thesame for all four restrictive rating labels? Test the appropriate hypotheses using a significance level of 0.05. (Let µ₁, M₂, M3, and μ4 be the truemean 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.)647Find the test statistic. (Round your answer to two decimal places.)F =710 8Use 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 isnot 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 reject Ho. The data do not provide convincing evidence that the mean rating associated with the game description by 12- to 13-year-oldboys 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-oldboys is not the same for all four restrictive rating labels.

Question

Accepted Answer

The test is to determine whether the data provides convincing evidence that the means of the rating…