8-4 Estimation Sample Size

Looking at the error as the limiting factor.. If E is determined to be a certain amount, then by solving the equation

Looking at the error as the limiting factor.. If E is determined to be a certain amount, then by solving the equation for E, it can be seen that This is for numerical data that has a mean and standard deviation

Looking at error as the limiting factor Of a binomial distribution…using the same idea…

Looking at error as the limiting factor Of a binomial distribution…using the same idea… and isolating n creates but…this implies we know p.

And if we don’t… Watch some algebra… Completing the square And since p is between 0 and 1, the maximum overall value of the expression will be….

Therefore When we have no estimate for p use Note: Some books say to take p and q as .5

Practice Suppose a candidate is planning a poll and wants to estimate voter support within 3% with 95% confidence. How large a sample is needed?

Round up to be safe Some books make the suggestion to use the Error equation and use .5 for phat and qhat for a “worst case scenario”. Notice that this works out the same way:

Round up to be safe Some books make the suggestion to use the Error equation and use .5 for phat and qhat for a “worst case scenario”. Notice that this works out the same way: Notice also that you don’t need a numerical formula to solve it. If you know the error formula, you have enough.