Word problem for statistics - sample size?

I have a question that I'm not sure how to go about doing it (not sure what formulas to use, etc). We're given the answer, but I would like to know how to arrive at the answer.





A survey asks a random sample of 1500 adults if they support an increase in tax from 5% to 6%, with the additional revenue going to education. Let p denote the proportion in the sample that say they support the increae. Suppose that 40% of all adults support the increase. How large a sample would be needed to guarantee that the standard deviation of p is no more than 0.01?


Answer: 2400

Word problem for statistics - sample size?
Standard Error of the Sample Proportion Equation





this equation is hard to write out, but when i put the numbers in it may make more sense. take the square root of everything after it


stand deviation = sqroot (proportion x 1- proportion)/ (sample)





0.01 = sqroot (0.4 x (1-.4)) / sample


0.01 = sqroot (.4 x .6) / sample


0.01= sqroot (.24) / sample





square both sides, so we can cancel out square root on the right





.0001 = .24/ sample





now multiply each side by sample





.0001 x sample = .24





divide by .0001 to find sample





sample = 2400