Planning a mobile gaming study

A recent study by a market research firm found that 38% of tablet gamers and 20% of mobile phone gamers play five or more hours per week.6 You decide to survey students at your large university and see how they compare.

(a) Using the sample proportion of just the tablet gamers from this previous study, what sample size of tablet gamers would you need for an estimate with a margin of error of 2.5% for 95% confidence?

(b) You expect the proportion of tablet gamers who play more than 5 hours to be higher in your population. What sample size would you need so that the margin of error is less than or equal to 2.5% regardless of the observed ?

(c) To implement this survey, you will need to take an SRS of students and first screen them to find out if they are tablet gamers. Suppose that only 20% of the students at your university are tablet gamers. What is the size of the initial sample of students that you will have to draw to obtain usable information from the sample size in part (b)?