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I'm trying to see if I'm applying the Sample Size concept correctly to my problem.

I have a survey where 20,000 people replied for a population size of 4,000,000. The question asked which product they like: 44% liked product A, 6% liked product B, and 50% liked product C.

So, a sample size of 20,000, a population size of 4,000,000, and a confidence level of 95% gives a 0.69% margin of error.

So, 1,200 people out of the 20,000 survey respondents said they liked product B.

Is it fair to say that out of the 4,000,000 population size that 240,000 will like product B?

Thank you in advance for any feedback or comments!

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In your survey you determined the fraction of people who like product A, B, and C and then you apply that fraction to your whole population and that is correct with one major caveat. You are assuming that your survey respondents are representative of your overall population. However, this is a big assumption to make. If there are factors that cause your survey audience to differ from the population. For example: the survey taker was positioned near where product A was sold in the store and thus sampled product A shoppers more than the other ones then there could be an issue in oversampling product A shoppers.

The problems that come from this are about extrapolating your sample to your population.

These mistakes don't need to be minor and could even lead one to incorrectly call a presidential election: https://en.wikipedia.org/wiki/Dewey_Defeats_Truman

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  • $\begingroup$ Thanks for your insight on this! The Wikipedia article was an interesting read. $\endgroup$ – Funstats4316 Oct 21 '19 at 15:17

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