Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken inn₁=38U.S. cities. The sample mean for these cities showed thatx₁=15.2%of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken inn₂=30U.S. cities. The sample mean for these cities showed thatx₂=19.3%of the young adults had attended college. From previous studies, it is known that₁=6.8%and₂=5.2%. Does this information indicate that the population mean percentage of young adults who attended college is higher? Use= 0.05.

a) What is the value of the sample test statistic? (Test the difference₁₂. Round your answer to two decimal places.)

b) Find (or estimate) theP-value. (Round your answer to four decimal places.)