You solve for random noise like that simply by looking at sufficiently large number of respondents, that's how basic statistics works. Any particular respondent

You solve for random noise like that simply by looking at sufficiently large number of respondents, that's how basic statistics works. Any particular respondent may have an unusually bad or good day, however, if there would be some real difference of a few percent in happiness conditional on religiosity, then given 4000 respondents it's extremely unlikely that the average responses would not reveal that.