When doing a sample size estimation for population proportion, what happens when the resultant confidence interval doesn’t contain the sample proportion that was used to come up with the sample size? For example:

For the next poll of the president's approval rating, we want to get a margin of error of 1% with 95% confidence. How many individuals should we sample? In the last poll his approval rate was 72%.

  • Confidence level: 95%
  • MoE: 1%
  • Sample proportion (p-hat): 72%
  • Sample size (n): 7,745

We conduct a new poll with sample size of 7,745, and the approval rate is 60%, so the confidence interval is 59 to 61% -- which doesn't contain the sample proportion of 72% that was used to estimate the sample size.

Does this mean the new approval rate of 59 to 61% has to be discarded, and a new poll with a more conservative sample proportion of 60% has to be done?

  • $\begingroup$ Your sample is whatever it is. Any preceding estimates of sample size are completely irrelevant. The situation is like searching for a coin you dropped on the floor. You guess it's under the bed and start searching there. Finally you find it under the desk. Should you give up and start over because you found it in a different location than you initially thought?? $\endgroup$ – whuber Oct 12 '16 at 13:32
  • $\begingroup$ Your coin analogy makes sense. Back to my example...so we should accept the new 59 - 61% approval rate, and for the subsequent poll, use a sample proportion of 60%? $\endgroup$ – Harper Oct 13 '16 at 2:42
  • $\begingroup$ Maybe--it all depends on how you think public opinion might be changing. It might help to know that the sample sizes needed are not very sensitive to the approval rates when the rates are near 50%. $\endgroup$ – whuber Oct 13 '16 at 16:29

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