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To find the standard error of the difference of two percentages, first we calculate each standard error separately. Beginning with the 194 towns on which we have information, the formula is s
p1
=
where n = the number of towns for which we have data (194), p = the proportion that were sundown (.995), and q = (1 - p) or .005. This standard error = .005 or 0.5%.
We also need to compute the standard error of the percentage of sundown towns among the 228 towns for which we have no information. Since we don’t know this percentage, we can assume just 90% will be, lower than the most likely estimate; such a conservative assumption provides a larger-than-likely standard error, which results in a more conservative overall estimate. Using the same formula, we substitute: n = 228, p = .9, and q = .1. This standard error = .020 or about 2%.
We then combine these two standard errors, using the formula s
(p1–p2)
=
find the standard error of the difference of two percentages, which = .0205 or 2.05%.