(a) State the sampling situation (a, b or c) for calculating the standard error

Question

(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.
Note: You must clearly show step-by-step solution to producing a confidence interval by hand. Use the t-procedures tool to find values for t-multipliers and standard errors.

Do you play mobile phone games for less 464 of the gamers surveyed in 2010 had than 60 minutes per week? recommended games to others. This group was asked what influenced them to 2009 Yes (521) Total recommend a game. They could choose as (659) many answers as they wished. The answers, 2010 Yes (554) Total (814) with the percentages, selecting them were: 33% From a trusted brand How often do you typically play on your 38% Controls simple to use mobile phone? 49% Easy to learn 2009 2010 86% Fun to play 284 Daily 40% Good value 2-3 times per week 296 119 36% Great graphics and sound 108 once a week 59 2-3 times a month 72 83 45% Is challenging 323 once a month or less 43 41% Lots of levels/modes 659 814 Total

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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