If no preliminary estimate of the population proportion give

If no preliminary estimate of the population proportion given for the people who have a disease and if they react positively to a new drug, how many medical files should you include in a random sample in order to be 95% sure that the point estimate will be within a distance of 0.03 from mean; that is, the (percent) error is 3%.?

Solution

In order to have a margin of error equal to 0.03 with 95% confidence, you want the following equation to be true: 0.03 = 1.96(p/sqrtN) Where p/sqrt(N) is the sample standard deviation. 1.96 is the z-value associated with the 95% confidence interval. If you don\'t know p, then use 0.5 which is the conservative approach. 0.03 is the margin of error you wish to hit. Now, solve for N: 0.03 = 1.96(0.50/sqrtN) sqrtN = 1.96(0.50)/0.03 = 98/3, next square both sides N = 1067.1 , so round up to the next highest integer 1068 to assure it will meet your margin of error of 0.03 So, make your sample size equal 1068 and this will produce a margin of error equal to 0.03.