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What is the statistical significance test that should be run to see if the results from a smaller group of those surveyed is significant and reflective of the larger group?

For instance: 1. Survey 1000 people and out of the 1000 people we also want to look at the group of 300 people that are within a certain demo. Would it be statistically significant to look at these results and assume that they are non-directional at 95% confidence? 2. And then from that, what should I run in order to see if proportions between the two is significant? Let's say out of the larger group of 1000, 100 answered yes to a questions. And out of those 300, 50 answered yes to a question.

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You would want to run a Pearson's Chi-Squared test to see if the proportions of each group are significantly different from each other. Just make sure that the groups are independent. So make sure to the 300 of the certain demographic are removed from the total sample and compared against the remaining 700 cases.

https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test

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