Question

The authors of the paper "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 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
4	4	6	8
7	5	4	6
6	4	8	6
5	6	6	7
3	3	10	7
6	5	8	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

α = 0.05.

Calculate the test statistic. (Round your answer to two decimal places.)

F = ______________

Answer 1

The following table is obtained:

	7+ label	12+ label	16+ label	18+ label
	4	4	6	8
	7	5	4	6
	6	4	8	6
	5	6	6	7
	3	3	10	7
	6	5	8	4
	4	3	6	10
	5	8	6	6
	10	5	8	8
	5	9	5	7
Sum =	55	52	67	69
Average =	5.5	5.2	6.7	6.9
i​Xij2​=	337	306	477	499
St. Dev. =	1.958	1.989	1.767	1.595
SS =	34.5	35.6	28.1	22.9
n =	10	10	10	10

The total sample size is N=40. Therefore, the total degrees of freedom are:

dftotal​=40−1=39

Also, the between-groups degrees of freedom are dfbetween​=4−1=3, and the within-groups degrees of freedom are:

dfwithin​=dftotal​−dfbetween​=39−3=36

First, we need to compute the total sum of values and the grand mean. The following is obtained

F value is 2.148