The authors of a paper titled \"Age and Violent Content Labels Make Video Games

Question

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.

(g) 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.

The appropriate hypotheses are:

The test statistic is:  

The p-value is associated with this test statistic is 0.0040. Based on this, the statistical decision is to:  ---

a) (Reject Ho) b) (FTR Ho) c) (Reject Ha) d) (FTR Ha )

(you have two attempts)

At the 0.05 level, we  --- that at least one mean rating differs significantly from the rest.
(you have two attempts)
a) have enough evidence to conclude

b) do not have enough evidence to conclude

c) have proven beyond doubt

d) have disproven beyond doubt

Group Sample Size Sample Mean Sample Std Dev 18+ label 22 7.1 1.56 16+ label 21 6.1 1.64 12+ label 18 5.9 1.74 7+ label 19 5 2.16

Explanation / Answer

a)

T=

=(7.1*22+6.1*21+5.9*18+5*19)

485.5

b)

n=

=22+21+18+19

80

c)

Xbarbar

=485.5/80

6.069

d)

SSB

=22*(7.1-6.069)^2+21*(6.1-6.069)^2+18*(5.9-6.069)^2+19*(5-6.069)^2

45.632

e)

SSE

=1.56^2*(22-1)+1.64^2*(21-1)+1.74^2*(18-1)+(2.16^2)*(19-1)

240.348

f)

g)

d) H0:u1=u2=u3=u4

Ha: at least one population mean is different

h)

test statistic:

F= 4.81

i)

p-value

0.0040

j)

(Reject Ho) as p-value<0.05

k)

At the 0.05 level, we -have enough evidence to conclude- that at least one mean rating differs significantly from the rest.

Source of Variation df Sum of Squares Mean Square F Treatment =4-1 45.632 =45.632/3 =15.210667/3.164210526 Error =79-3 240.48 =240.48/76 X Total =80-1 =I67+I68 X X

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