All multiple choice questions have two submissions.The authors of a paper titled "Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth" 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 summary data shown below are the ratings of 12- to 13-year-old boys for how much they wanted to play the game on a scale of 1 to 10. You can assume that boys were assigned at random to one of the four age label treatments (7+, 12+, 16+, 18+) and that ratings were normally distributed.

Group |
Sample Size |
Sample Mean |
Sample Std Dev |

7+ label |
10 |
6 |
2.04 |

12+ label |
10 |
7.1 |
1.58 |

16+ label |
10 |
7.9 |
1.55 |

18+ label |
10 |
8 |
1.65 |

(a) What is the sum of all observations in the data set? T =

(b) What is the grand mean?

=

(use three decimals in your answer) (c) Calculate the treatment sum of squares, which is a measure of

sample variation.

SSTr =

(use four decimals in your answer) (d) Calculate the error sum of squares, which is a measure of

sample variation.

SSE =

(use four decimals in your answer) (e) Complete the ANOVA table. Note that you've already found two of the three sums of squares.

Use four decimals for the sums of squares and means squares, then round the F test statistic to 2 decimals.
(f) Do 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? Test the appropriate hypotheses using a significance level of 0.01.

The appropriate hypotheses are:

The significance level is:

The test statistic is:

The p-value is:

The statistical decision is to:

At the 0.01 level, we

conclude that at least one of true mean ratings is different.