Given a random variable $X$ which can take values on $[0,1]$. I am interested in calculating the confidence values for the mean estimator. We know that the mean is normally distributed and can calculate the regular confidence value, but they lie outside of $[0,1]$. How do you deal with this do you intersect the confidence value with the range $[0,1]$?
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Mean in this case is proportion, so a proportion CI. – user2974951 Oct 09 '19 at 11:11
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Great. if you make it an answer i can accept it. – user3680510 Oct 09 '19 at 12:30
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@user2974951 In what sense would that mean be a "proportion"? There aren't any counts involved here. – whuber Oct 09 '19 at 12:59
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Closely related: https://stats.stackexchange.com/questions/357843, https://stats.stackexchange.com/questions/21854 (concerning proportions, btw), https://stats.stackexchange.com/questions/223507 (also proportions). – whuber Oct 09 '19 at 13:01
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@whuber I don't know, but we can pretend it is. – user2974951 Oct 09 '19 at 13:23
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@user2974951 That requires justification which doesn't appear to be present in the information given. After all, we can pretend the moon is a small ball of green cheese, but that won't help us design a rocketship to take us there. In the present case, if the values of $X$ really are proportions, then they have variances that depend on those proportions (as well as on the underlying sample sizes), which will strongly influence the choice of confidence interval procedure. – whuber Oct 09 '19 at 13:29