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I have a sample of observations (n) representing individual evaluations (positive/negative) of pieces of text (n texts). Each individual can evaluate more texts (thus there are m individuals with m < n). I would like to test if the population mean (ratio of positive evaluations) is $>0.5$.

My initial idea is to compute the ratio of positive evaluations per individual ($\bar{x_{i}}$) and then to do a proportion test for the mean $\bar{x_{i}}$, weighted by the number of data points used in computing $\bar{x_{i}}$. I have found a way how to do this in R for a t-test (https://www.rdocumentation.org/packages/weights/versions/0.85/topics/wtd.t.test) but not for z-test or chi-square test which are better suited for proportions. Does anybody have some suggestions? I would especially be interested in an R function that I could use.

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