Margin of Error
The cost of obtaining sample measurements and the accuracy of the sample estimate are generally conflicting requirements in designing a sample survey. Suppose it is desired to obtain the proportion of people who are problem gamblers to within +0.002 (this is the ‘margin of error’), using a 95% confidence interval. In the past it has been estimated that the prevalence of problem gambling is around 1%.
(a) How large a sample would be needed to secure this degree of accuracy?
(b) Suppose it costs $2.50 to question each person included in the sample, and the sponsors of the surveys are prepared to pay $2,500 for the exercise. What is the best accuracy they can expect, using a 95% confidence interval (3dp)?
(c) Using the sample size from (a), estimate the margin of error that the survey would achieve if it were used to estimate the proportion of people who gamble at all. Use the conservative p=0.5 when calculating your answer.
