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Estimating Sample Size Based on Error in Polling Data

This text explores the process of estimating the appropriate sample size for a poll while considering error as the limiting factor. It discusses how to determine the sample size needed to achieve a certain margin of error (E) with a specified confidence level (e.g., 95%). The approach incorporates both numerical data, including mean and standard deviation, and binomial distribution concepts. Additionally, it highlights the importance of rounding up sample estimates to ensure accuracy and acknowledges "worst case scenarios" as a basis for estimation in polling practices.

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Estimating Sample Size Based on Error in Polling Data

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Presentation Transcript

  1. 8-4 EstimationSample Size

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

  3. 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

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

  5. 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.

  6. 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….

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

  8. 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?

  9. 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:

  10. 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.

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