Final answer:
The factor used to adjust for increased sampling variation in both the mean (x) and proportion (p) when correcting for finite population is the Finite Population Correction Factor (option c).
Step-by-step explanation:
The factor used to adjust for increased sampling variation in both the mean (x) and proportion (p) when correcting for finite population is the Finite Population Correction Factor (option c). When the population size is relatively small compared to the sample size, the finite population correction factor is applied to reduce the sampling variation. By incorporating this factor, the standard deviation is adjusted to account for the limited population size, resulting in a more accurate estimation of the mean and proportion.