The average size of a farm in Indiana County, Pennsylvania, is 191 acres. The average size of a farm in Greene County, Pennsylvania, is 199 acres. Assume the data were obtained from two samples with standard deviations of 38 and 12 acres, respectively, and sample sizes of 8 and 10, respectively. Can it be concluded at α = 0.05 that the average size of the farms in the two counties is different? Assume the populations are normally distributed.

(Perform this hypothesis test with both the traditional method and the p-value method and label which technique is the traditional method and which one is the p-value method.)