olay the game. The description also induded 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 7 12+ label 79: 958 16+ label 7 6 18+ label 9 6 87689 10 8 10 A USE SALT 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 s Ha, and , be the true mean atings 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: at least two of the four 's are different OH, : , - - H, " . H,: at least three of the four a's are different O H: all four of the 's are different H, : " " H " Ha H,: all four of the 's are different H, : at least two of the four 's are different Find the test statistic. (Round your answer to two decimal places.) Jse technology to find the P-value. (Round your answer to four decimal places.) value - State the conclusion in the problem context. O We reject H. 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 H. 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 Ha. 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section: Chapter Questions
Problem 13PT
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Question
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
7
76
5 5 8
6 1
4
12+ label
8
79
8
4
16+ label
9
7 4
8
9
6
18+ label
10
9 6
8
7 6
9
10
n USE SALT
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 u,, u,, Ha, 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.)
State the appropriate null and alternative hypotheses.
O H. : at least two of the four u's are different
H : 41 = H2 = Mz = H4
O H. : H, = H2 = !3= H4
H : at least three of the four u's are different
O H, : all four of the u,'s are different
O Ho : 41 = M2 = 43 = 44
H : all four of the u,'s are different
O H, : 4, = 42 = !3 = H4
H : at least two of the four u'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.
O We reject H.. 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 H.. 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 Hp. 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 H,. 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.
Transcribed Image Text: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 7 76 5 5 8 6 1 4 12+ label 8 79 8 4 16+ label 9 7 4 8 9 6 18+ label 10 9 6 8 7 6 9 10 n USE SALT 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 u,, u,, Ha, 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.) State the appropriate null and alternative hypotheses. O H. : at least two of the four u's are different H : 41 = H2 = Mz = H4 O H. : H, = H2 = !3= H4 H : at least three of the four u's are different O H, : all four of the u,'s are different O Ho : 41 = M2 = 43 = 44 H : all four of the u,'s are different O H, : 4, = 42 = !3 = H4 H : at least two of the four u'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. O We reject H.. 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 H.. 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 Hp. 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 H,. 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.
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