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 data below for 12- to 13-year-old boys are fictitious, but 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	12+ label	16+ label	18+ label
7	8	7	10
7	7	9	9
6	10	8	6
5	5	6	8
5	7	7	7
8	9	5	6
6	5	8	8
1	8	9	9
2	4	6	10
4	7	7	8

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 0.05.

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

B. What can be said about the P-value for this test?

P-value > 0.1000
.050 < P-value < 0.100   
0.010 < P-value < 0.0500
.001 < P-value < 0.010
P-value < 0.001

C.
Reject H₀. 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.
Reject H₀. 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.    
Fail to reject H₀. 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.
Fail to reject H₀. 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.

Answer 1

For the given data using Anova single factor in Excel we get output as

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
7+ label	10	51	5.1	4.988889
12+ label	10	70	7	3.555556
16+ label	10	72	7.2	1.733333
18+ label	10	81	8.1	2.1
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	47.7	3	15.9	5.138241	0.004633	2.866266
Within Groups	111.4	36	3.094444
Total	159.1	39

From the above output

( A ) Answer : test statistic ( F ) = 5.14

P value = 0.0046

( B ) Answer : .001 < P-value < 0.010

P value < l.o.s

i.e ., 0.0046 < 0.05

So reject H0

( C ) Answer : Reject H₀. 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