Hypothesis
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What percentage of times will the mean (population proportion) not be found within the confidence interval?
The Poincaré Conjecture.
The answer depends on how rare or common the selected trait is. For something that is very rare, you will need a much larger sample to get a reasonable estimate of proportion.
One possible conjecture is that their sum is 27. The conjecture is patently false, but that does not stop it being a conjecture.
My conjecture is that the sum is 67. A conjecture does not have to be true, or even plausible. You should be able to test it. If it is found to be true then in is no longer a conjecture, if it is found to be false, it is rejected - and so no longer a conjecture. If it cannot be proved either way, it remains a conjecture.