In 2010, PopCap Games commissioned a survey of adult mobile phone gamers in the
ID: 3229642 • Letter: I
Question
In 2010, PopCap Games commissioned a survey of adult mobile phone gamers in the United
States and in the United Kingdom. A similar survey was also carried out in 2009. Some of the
information from the survey is given below:
Do you play mobile phone games for less
than 60 minutes per week?
2009: Yes (521) Total
(659)
2010: Yes (554) Total (814)
How often do you typically play on your
mobile phone?
2009 2010
Daily 86 284
2-3 times per week 119 296
once a week 59 108
2-3 times a month 72 83
once a month or less 323 43
Total 659 814
464 of the gamers surveyed in 2010 had
recommended games to others. This group
was asked what influenced them to
recommend a game. They could choose as
many answers as they wished. The answers,
with the percentages, selecting them were:
33% From a trusted brand
38% Controls simple to use
49% Easy to learn
86% Fun to play
40% Good value
36% Great graphics and sound
45% Is challenging
41% Lots of levels/modes
(a) State the sampling situation (a, b or c) for calculating the standard error of the difference in the
following scenarios:
(i) estimating the difference between the proportion of gamers that played for less than 60
minutes per week in 2009 and the proportion of gamers that played for less than 60
minutes per week in 2010.
(ii) estimating the difference between the proportion of gamers that played for at least 60
minutes per week in 2010 and the proportion of gamers that played daily in 2010.
(iii) estimating the difference between the proportion of gamers that played daily in 2010
and the proportion of gamers that played 2-3 times per week in 2010.
b) For gamers who recommend games to others, calculate and interpret a 95% confidence
interval for the difference between the proportion of all gamers who, in 2010, would have
recommended a game that is fun to play and the proportion of all gamers who, in 2010,
would have recommended a game that is easy to learn.
Explanation / Answer
(a) (i) estimating the difference between the proportion of gamers that played for less than 60 minutes per week in 2009 and the proportion of gamers that played for less than 60 minutes per week in 2010.
Two independent sample proportions.
(ii) estimating the difference between the proportion of gamers that played for at least 60 minutes per week in 2010 and the proportion of gamers that played daily in 2010.
One sample with multiple inclusive response categories.
(iii) estimating the difference between the proportion of gamers that played daily in 2010 and the proportion of gamers that played 2-3 times per week in 2010.
One sample with multiple mutually exclusive response categories
(b) Difference between the proportion of all gamers who, in 2010, would have recommended a game that is fun to play and the proportion of all gamers who, in 2010, would have recommended a game that is easy to learn = 86 - 49 = 37
Standard error = sqrt{ [ P1(1 - P1) / n1 ] + [ P2(1 - P2) / n2 ] }
= sqrt{ [ 0.86(1 - 0.86) / 464 ] + [ 0.49(1 - 0.49) / 464 ] } = 0.02825
t - value for 95% confidence interval = 1.96
margin of error = 1.96 * 0.02825 = 0.05537
95% confidence interval is (37 - 0.05537, 37 + 0.05537)
= (36.94463, 37.05537)
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