How was that sentence constructed? [Where did the numbers come from?]

Part of this is easy: The .80 (the claimed “center value” of the proposed proportion of the population that “yes” had egg spots) is just the proportion of the SAMPLE that had egg spots.

The other part (the margin of error of .09) is certainly more confusing. Where this number came from is not at all clear (YET).

Part of this is easy: The .80 (the claimed “center value” of the proposed proportion of the population that “yes” had egg spots) is just the proportion of the SAMPLE that had egg spots.