A physicians' group is interested in testing to determine whether more people in small towns choose a physician by word of mouth in comparison with people in large metropolitan areas. A random sample of 1,000 people in small towns reveals that 850 chose their physicians by word of mouth; a random sample of 2,500 people living in large metropolitan areas reveals that 1,950 chose a physician by word of mouth.
Conduct a one-tailed test aimed at proving that the percentage of popular recommendation of physicians is larger in small towns than in large metropolitan areas. Use α = 0.01.